Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? 6 meters cubed 7 meters cubed 14 meters cubed 28 meters cubed

Answer 1

14 meters cubed

Explanation:

Volume of cylinder:

pi × r² × (2r)

2pi × r³ = 21

pi × r³ = 10.5

Volume of sphere:

(4/3) × pi × r²

(4/3) × 10.5

14 m³

Answer 2

C. 14 metres cubed

Explanation:

The volume of a sphere is denoted by:
`V=(4)/(3) \pi r^3`, where r is the radius, while the volume of a cylinder is denoted by:
`V=\pi r^2h`, where r is the radius and h is the height.

Here, we know that the sphere and cylinder have the same radius and height. However, the "height" of the sphere is technically just the diameter, which is twice the radius. So, h = 2r. We know the volume of the cylinder is 21, so:

`V=\pi r^2h=\pi r^2*2r=2\pi r^3`

`21=2\pi r^3`

πr³ = 21/2 = 10.5

Now plug this into the volume of a sphere formula:

`V=(4)/(3) \pi r^3`

`V=(4)/(3) *10.5=14`

The answer is C, 14 metres cubed.