Question

The volume of cylinder is 504 pi cm^(3) & height is 14cm Find the curved surface area 8 total surface area.

Answer 1

The Solution:

The correct answers are:

Curved surface area = 527.79 squared centimeters

Total surface area = 753.98 squared centimeters.

Given that the volume of a cylinder with height 14cm is

`504\pi cm^3`

We are required to find the curved surface area and the total surface area of the cylinder.

Step 1:

We shall find the radius (r) of the cylinder by using the formula below:

`V=\pi r^2h`

In this case,

`\begin{gathered} V=\text{volume =504}\pi cm^3 \\ r=\text{ radius=?} \\ h=\text{ height =14cm} \end{gathered}`

Substituting these values in the above formula, we get

`504\pi=\pi r^2*14`

Finding the value of r by first dividing both sides, we get

`\begin{gathered} (504\pi)/(14\pi)=r^2 \\ \\ r^2=36 \end{gathered}`

Taking the square root of both sides, we get

Step 2:

We shall find the curved surface area by using the formula below:

`\text{CSA}=2\pi rh`

Where

Substituting these values in the formula above, we have

`\text{CSA}=2*6*14*\pi=168\pi=527.788\approx527.79cm^2`

Step 3:

We shall find the total surface area by using the formula below:

`\text{TSA}=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh`

Where

TSA= total surface area and all other parameters are as defined earlier on.

Substituting in the formula, we get

`\text{TSA}=(2\pi*6^2)+(2\pi*6*14)=72\pi+168\pi`
`\text{TSA}=240\pi=753.982\approx753.98cm^2`

Therefore, the correct answers are:

Curved surface area = 527.79 squared centimeters

Total surface area = 753.98 squared centimeters.