Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 centimeters cubed.

A sphere with height h and radius r. A cylinder with height h and radius r.

What is the volume of the sphere?
A.12 centimeters cubed
B.24 centimeters cubed
C.36 centimeters cubed
D.54 centimeters cubed

Answer 1

The answer is A

Step-by-step explanation:

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Answer 2

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 centimeters cubed.-The volume of the sphere is (A)12 centimetres cubed

Step-by-step explanation:

Step 1

The formulas for calculating the volume of a cylinder and and the volume of a sphere, are:

`v_(c) =`π
`r_(2) h`

`v_(s) =4/3` π
`r^(2) h`

Here r is the radius and h is the height.

Step 2

Given that the sphere and the cylinder have the same radius and height. As per the definition, the height of the sphere is twice its radius. Thus we can write as the height of the cylinder is:

`h=2r`

Step 3

Now we substitute the value obtained it into the formula for to calculate the volume of a cylinder

`v_(c) =`π
`r^(2) (2r)`

`v_(c) =2`π
`r^(3)`

Step 4

So ,we can write that

`v_(s) =4/3(v_(c) /2)`

(π
`r^(3)`=
`v_(c) /2`)

Step 5

`v_(s) =4/3(18/2)\\v_{s=12 cm`

The volume of the sphere is (A)12 centimetres cubed