Answers
Given for the cone:
base radius: 3aperpendicular height: 4agiven for the spheres:
radius: aFind volume of cone:
[tex]\sf \hookrightarrow \dfrac{1}{3} \pi r^2h[/tex]
[tex]\sf \hookrightarrow \dfrac{1}{3} \pi (3a)^2(4a)[/tex]
[tex]\sf \hookrightarrow 12\pi a^3[/tex]
Find volume of sphere:
[tex]\sf \hookrightarrow \dfrac{4}{3} \pi r^3[/tex]
[tex]\sf \hookrightarrow \dfrac{4}{3} \pi a^3[/tex]
Divide volume of cone by volume of sphere:
[tex]\sf \hookrightarrow \dfrac{12\pi a^3}{ \dfrac{4}{3} \pi a^3}[/tex]
[tex]\rightarrow 9[/tex]
Therefore proved 9 such spheres can be made using the metal cone.
We know that volume of cone is [tex]12\pi a^3[/tex]
[tex]\sf \rightarrow 12\pi a^3 = 12936[/tex]
[tex]\sf \rightarrow a^3 = \dfrac{12936}{12\pi}[/tex]
[tex]\sf \rightarrow a = \sqrt[3]{\dfrac{12936}{12\pi}}[/tex]
[tex]\sf \rightarrow a =7[/tex]
Therefore the radius of sphere is 7 cm
Related Questions
Solve the problem. 6/y= 9/24
Answers
Answer: y = 16 should be your answer.
Answer:
Y=16
Step-by-step explanation:
Division is the method
How many parallel pairs are in a trapezoid
Answers
Answer:
the answer would be one pair
y + 8.63 = 11.001
Help, what does y equal to?!??!
50 points to whoever answers this question!!!!!
Answers
Answer:
2.371
Step-by-step explanation:
subtract 8.63 to 11.001
Find the value of x.
Answers
Answer:
x=9.6
Step-by-step explanation:
First, we have to find a similarity statement including x with 3 other values. One that we can do is long leg/hypotenuse=long leg/hypotenuse. If we use the small triangle we can get x/12 (x being long leg, 12 being hypotenuse), and using the big triangle we can get 16/20 (16 being long, 12 being hypotenuse). So, if x/12=16/20, we can solve and get that x=9.6
15 1/3 - 2 5/8 I need so much help on this type of stuff anyone pls tutor me
Answers
Answer: 12.7083333333
Step-by-step explanation: First you turn both numbers into a inproper fraction. Then you subtract and simplify.
hello help me with this question thanks in advance
Answers
[tex]\bold{\huge{\underline{ Solution \:1 }}}[/tex]
Figure 1 :-Here, we
One triangle and AB acts as a bisector for RT and ST. The length of AT and AR are 15 and 5The length of BT and BS are 12 and 4By using basic proportionality theorem :-
This theorem states that if a line which is parallel to the side of triangle intersect other to sides then the line which divides the other two sides are in proportion that means the ratios are equalThat is,
[tex]\sf{\dfrac{ AT}{RT }}{\sf{=}}{\sf{\dfrac{BT}{ST}}}[/tex]
Subsitute the required values,
[tex]\sf{\dfrac{ 8 }{ 8 + 11 }}{\sf{=}}{\sf{\dfrac{7}{7 +10}}}[/tex]
[tex]\sf{\dfrac{ 8 }{ 19}}{\sf{=}}{\sf{\dfrac{7}{17}}}[/tex]
[tex]\sf{\dfrac{ 8 }{ 19}}{\sf{≠}}{\sf{\dfrac{7}{17}}}[/tex]
Hence, AB is not parallel to RS
Figure 2 :-Here, we have
One triangle and AB acts as a bisector for RT and ST. The length of AT and AR are 8 and 11The length of BT and BS are 7 and 10By using basic proportionality theorem :-
That is,
[tex]\sf{\dfrac{ AT}{RT }}{\sf{=}}{\sf{\dfrac{BT}{ST}}}[/tex]
Subsitute the required values,
[tex]\sf{\dfrac{ 15 }{ 15 + 5 }}{\sf{=}}{\sf{\dfrac{12}{16}}}[/tex]
[tex]\sf{\dfrac{15 }{ 20}}{\sf{=}}{\sf{\dfrac{12}{16}}}[/tex]
[tex]\sf{\dfrac{ 3}{ 4}}{\sf{=}}{\sf{\dfrac{3}{4}}}[/tex]
Hence, AB is parallel to RS
[tex]\bold{\huge{\underline{ Solution\: 2}}}[/tex]
Here, we have
Triangle ABC and DE || BC The length of AB = 12 , AD = 4 , DE = 6 and AC = 24 .Part 3 :-
By using basic proportionality theorem,
This theorem states that if a line which is parallel to the side of triangle intersect other to sides then the line which divides the other two sides are in proportion that means the ratios are equalThat is,
[tex]\sf{\dfrac{ AD}{AB }}{\sf{=}}{\sf{\dfrac{AE}{AC}}}[/tex]
Subsitute the required values,
[tex]\sf{\dfrac{ 4}{12 }}{\sf{=}}{\sf{\dfrac{AE}{24}}}[/tex]
[tex]\sf{\dfrac{ 4}{12 }}{\sf{{\times} 24= AE}}[/tex]
[tex]\sf{ AE = 4 {\times} 2 }[/tex]
[tex]\sf{ AE = 8 }[/tex]
Hence, The length of AE is 8
Part 4 :-Again , By using Basic proportionality theorem :-
That is
[tex]\sf{\dfrac{ AD}{AB }}{\sf{=}}{\sf{\dfrac{DE}{BC}}}[/tex]
Subsitute the required values,
[tex]\sf{\dfrac{ 4}{12 }}{\sf{=}}{\sf{\dfrac{6}{BC}}}[/tex]
[tex]\sf{\dfrac{ 1}{3 }}{\sf{=}}{\sf{\dfrac{6}{BC}}}[/tex]
[tex]\sf{ BC = 6 {\times} 3 }[/tex]
[tex]\sf{ BC = 18 }[/tex]
Hence, The length of BC is 18 .
Find the value of X
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answers
Answer:
11[tex]\sqrt{2}[/tex]
Step-by-step explanation:
The given shape is a right triangle, to find the value of x we can use Euclidian Theorem:
x^2 = 14*(14+4)
x^2 = 280 find the root for both sides
x = 11[tex]\sqrt{2}[/tex]
10) Consider the function f(x) = x2 shown, which describes the graph of the function? A) increasing B) decreasing C) increasing then decreasing D) decreasing the increasing
Answers
The function f(x) = x^2 is a quadratic function
The graph is (D) decreasing the increasing
How to describe the function?The function is given as:
f(x) = x^2
From the graph of the function, we can see that the function values decreases then increases.
Hence, the statement that describes the graph is (D) decreasing the increasing
Read more about functions at:
https://brainly.com/question/15602982
In a circle, a chord is 16 cm in length and 6 em from the center of a circle. Find the length of the
diameter of the circle.
Answers
Answer:
Step-by-step explanation:
radius = r
r² = (16/2)² + 6² = 100
r = 10, diameter = 2r = 20 cm
Which equation
represents a line that passes through (2, -1/2) and has a slope of 3?
Answers
Answer:
y = 3x - 6 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We can use y = m x + c to find the equation of the line.
Here,
m ⇒ slope
c ⇒ y - intercept
They have already given the slope of the line.
m = 3
And now we have to find the y - intercept using the given coordinates.
( 2 , - 1/2 ) ⇒ ( x , y )
Let us find now.
y = m x + c
-1/2 = 3 × 2 + c
-0.5 = 6 + c
-0.5 - 6 = c
-6.5 = c
-6 1/2 = c
Now let us write the equation of the line.
y = m x + c
y = 3x - 6 [tex]\frac{1}{2}[/tex]
The contents of each box of books weighs 18 pounds. There are 24 books in each box. How much does each book weigh?
Answers
each
please help me solve for x
Answers
[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]
The shown pair of angles are Co interior angle pair, therefore the sum of those angles is 180°
[tex]\qquad \sf \dashrightarrow \: 130 \degree + 7x + 1 \degree = 180 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \: 131 \degree + 7x = 180 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \: 7x= 180 \degree - 131 \degree[/tex]
[tex]\qquad \sf \dashrightarrow \: 7x= 49 \degree [/tex]
[tex]\qquad \sf \dashrightarrow \: x=49 \degree \div 7[/tex]
[tex]\qquad \sf \dashrightarrow \: x=7 \degree [/tex]
The required value of x is 7°
If a ray stands on a line, then the sum of two adjacent angles so formed is 180 .
7x + 1 + 130 = 180 7x + 131 = 180 7x = 180 - 131 7x = 49 x = 49/ 7 x = 7Hope it helps ~
Please help me need ASAP
Answers
Answer:
B
Step-by-step explanation:
Because you will divide U in X the give you correct answer.
if a car covers 54km in an hour how much distance will it cover in 40 minutes
Answers
Answer:
It cover 36 km in 40 minutes
Step-by-step explanation:
Write the equation of the circle that has a center of (-7, 17) with
a radius of V19.
Answers
I think your question seems to be :-
Write the equation of the circle that has a center of (-7, 17) with a radius of √19
So , as we know that the equation of circle with centre at (h,k) and radius r is given by [tex]{\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}}[/tex] . Now , using same concept in this question ;
[tex]{:\implies \quad \sf \{x-(-7)\}^{2}+(y-17)^{2}=(\sqrt{19})^{2}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{(x+7)^{2}+(y-17)^{2}=19}}}[/tex]
This is the required equation of Circle
Dario purchased a party size sub, and he decides to share it with 3 of his friends. So, he cuts the sub into 4 equal pieces. However, another one of his friends also showed up, and there are now 5 people in total.
Part A --
Now that the sub will be shared equally among 5 people, will each person get more or less sub? Briefly state why you think so.
Part B --
Dario decides to take each one of the 4 pieces and share it equally among the 5 of them.
First, he divides one piece into 5 equal parts and shares it, then the next one, and so on.
What fraction of the party size sub did each person get after all the parts were shared out? Briefly explain your reasoning.
Answers
Answer:
less sub
if there is less, then you could also divide it into 20 pieces, and give 4 pieces per friend
Step-by-step explanation:
3. Higher Order Thinking The
lengths of the pencils are
given at the right.
Write and solve a two-step
problem about the pencils.
6 cm
8 cm
10 cm
Answers
The lengths of the three pencils form a right-triangle, and the two-step problem is:
6^2 + 8^2 = 10^2100 = 100How to write the two-step problemThe lengths of the pencils are given as:
6cm, 8cm and 10cm
Using the Pythagoras theorem, we have:
6^2 + 8^2 = 10^2
Evaluate the exponents
100 = 100
Hence, the lengths of the three pencils form a right-triangle
Read more about two-step problem at:
https://brainly.com/question/24590763
Which of the following describes the transformation?
A. Reflection over the X axis
B. Reflection over the Y axis
C. Rotation 90° clockwise about the origin
D. Rotation 180° clockwise about the origin
Answers
Answer:
D
Step-by-step explanation:
I hope this helps!
Answer:
B
Step-by-step explanation:
Imagine a mirror at the Y-axis, the two triangles will be mirror-image of each other. So the CORRECT answer is B. Reflection over the Y axis
Witch is greater 76.201 or 76.187
Answers
Answer:
76.201 is greater than 76.187
A house plan shows a scale of 1:40. If the rectangular lounge room of the house is to measure 4.5 metres by 6.3 metres, What are the dimensions of the room on the plan?
Answers
Answer:
.112 m by .157m OR 4.43 by 6.20 in
Step-by-step explanation:
The scale is 1:40, meaning that if the house plan shows 1 of something, the real life version is 40 times larger. Given this information:
4.5 m by 6.3 m is the ACTUAL SIZE.
Given this, we need to divide by 40 to get the room PLAN.
0.1125 by 0.1575 meters, OR 4.42913386 by 6.2007874 inches.
Simplifed,
.112 m by .157m OR 4.43 by 6.20 in
:)
-3x- 1>8 solve and then graph the equation
Answers
Answer:
x<-3
Step-by-step explanation:
-3x-1>8
Add +1 on both sides
-3x>9
Divide by -3 on both sides (don't forget to switch the inequality sign when you multipy or divide by a negative)
x<-3
(-1)[p-(-5)(-9)]+(p+q)(-2) if p =-3 and q =7
Answers
Answer:
40
Step-by-step explanation:
Substitute the value of the variable into the expression and simplify.
Hope it helps!!!!!Brainliest pls!!!!!What is the value of the expression below when y=4y=4? 3y^2 +y+8 3y 2 +y+8
Answers
Answer:
1. 18
2. 13.5
3. 3rd choice
4. 2nd choice
5. 18.6
6.3m + 8
7. 5x2 + y
i hope this work for you
1
If 3 dogs equally share pound of dog
food what share will each dog get?
2
Answers
Answer:
.333 pounds hope this helps
A shipping container is in the form of a right rectangular prism, with dimensions of
20 ft by 8 ft by 9 ft 9 in. If the container holds 359 cubic feet of shipped goods, what
percent is full? Round your answer to the nearest whole number if necessary.
Answers
Answer:
23%
Step-by-step explanation:
1) Find the area of the container. (20*8*9.9)
2) Divide 359 by 1584 (the area) to find the percent
3) Round up the percent and you get 23%.
2. A bike costs
A
$650. During
Sale it is marked
Idown 35%. What is
the sale price of the
bike?
I need the process as well, Please answer fast!!!
Answers
Answer:
$422.50
Step-by-step explanation:
Given the following question:
35% of 650
To find the answer we must first calculate 35% of 650 by using the formula to calculate percentages. Then we will subtract that answer from the original price of the bike, which will give us our answer.
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{35\times650}{100}[/tex]
[tex]35\times650=22750[/tex]
[tex]22750\div100=227.5[/tex]
[tex]=227.50[/tex]
Now subtract from the original price:
[tex]650[/tex]
[tex]650-227.5=422.5[/tex]
[tex]=422.50[/tex]
The bike after a 35% markdown will cost "$422.50."
Hope this helps.
70 is 140% of what number?
Answers
Answer:
Step-by-step explanation:
simply 70×100÷140, which will give you the answer.
Answer:
50
Step-by-step explanation:
mental math look at my profile if you want to trust me or not
There were 10 tables at a company luncheon. The company ordered
25 pizzas. If the same amount of pizza was served at each table, how much
pizza did each table get? Give your answer as a fraction or mixed number
and also as a decimal.
Answers
Answer:
Fraction: [tex]2\frac{1}{2}[/tex]
Decimal: 2.5
Step-by-step explanation:
Divide the total number of pizzas by the number of tables.
[tex]\frac{25}{10} = \frac{5}{2} = 2\frac{1}{2} = 2.5[/tex]
Jace and Lianna each baked a loaf of bread. jace cut his loaf into halves and lianna cut her loaf into thirds. Jace says they can use their loaves of bread to show the 1/2 is less than 1/3. lianna says they cant. who is correct explain why or why not
Answers
Answer:
Jace is correct they can use their loaves of bread to show 1/2 is less than 1/3. Because they have 2 loaves of bread
a washer and dryer cost a total of 993. the cost of the washer is two times the cost of the dryer. find the cost of each item
Answers
Let the price of the dryer = X
The washer is 2 times that so you would have 2x
Now you have X + 2x = 993
Simplify:
3x = 993
Divide both sides by 3:
x = 331
The dryer cost 331
The washer cost 2 x 331 = 662