Question

10 The cylinder shown has a volume of 120 cubic inches and its

height is equal to its radius. The cylinder and the sphere

shown have the same radius.

Which is the volume of the sphere?

A

40 cubic inches

B

90 cubic inches

C

160 cubic inches


D

360 cubic inches

Answer 1

Answer:

$V = \pi r^2 h = \pi r^3$

And we can solve for the radius:

$r = (\frac{V}{\pi})^{1/3}$

And replacing we got:

$r = (\frac{120 in^3}{\pi})^{1/3} = 3.368 in$

And the volume for a sphere is given by:

$V = \frac{4}{3} \pi r^3$

And replacing we got:

$V = \frac{4}{3} \pi (3.368 in)^3 = 160 in^3$

And the best option for this case is:

C  160 cubic inches

Step-by-step explanation:

For this case we know that the volume for the cylinder is 120 in^3. We know that the radius of this cylinder is equal to the height so then the volume can be founded with this formula:

$V = \pi r^2 h = \pi r^3$

And we can solve for the radius:

$r = (\frac{V}{\pi})^{1/3}$

And replacing we got:

$r = (\frac{120 in^3}{\pi})^{1/3} = 3.368 in$

And the volume for a sphere is given by:

$V = \frac{4}{3} \pi r^3$

And replacing we got:

$V = \frac{4}{3} \pi (3.368 in)^3 = 160 in^3$

And the best option for this case is:

C  160 cubic inches