Question

This cylinder has a volume of 12pi cubic inches and a diameter of 4 inches. Find the cylinder’s radius and height.

Answer 1

Answer:

radius r = 2 inches  and height (h) = 3 inches

Step-by-step explanation:

step:-1

The Volume of the cylinder is $V = \pi r^{2} h$.............(1)

Given volume of the cylinder is 12 pi cubic inches

and diameter is 4 inches

we know that the diameter is two times of radius

that is d = 2 r

so $r = \frac{d}{2}$

$V = \pi (\frac{d}{2})^2 h$......(2)

Step 2 :-

substitute V = 12 pi cubic inches and diameter d = 4 inches in equation (2)

$12\pi = \pi (\frac{4}{2} )^2$h

after simplification, and cancellation 'pi' on both sides , we get

$12 = 4h$

h = 3

Step 3:-

now substitute h = 3 and volume of the cylinder is 12 pi in equation (1)

$V = \pi r^{2} h$

$12\pi = \pi (r)^2(3)$

cancellation 'pi' on both sides, we get

$r^{2} = 4$

$r=2$

the radius of cylinder is 2 and height of the cylinder is 3

Answer 2

Answer:

The first person was right but this is a more easier explanation

Step-by-step explanation: