How to find the surface area of a cylinder - ISEE Upper Level Mathematics Achievement

Card 0 of 2

Question

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Answer

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Find surface area with the following formula:

$A=2\pi r h +2\pi r^2$

This works because we are adding the area of the two bases to the area of the side.

Plug in and simplify:

$A=2\pi (12mm)(6mm) +2\pi (12mm)^2=144\pi mm^2+288\pi mm^2=432 \pi mm^2$

Compare your answer with the correct one above

Question

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

Answer

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 14cm. We also know that the diameter is two times the radius. Therefore, the radius is 7cm.

We know the height of the cylinder is 8cm.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (7\text{cm})^2 \cdot 8\text{cm}$

$V = \pi \cdot 49\text{cm}^2 \cdot 8\text{cm}$

$V = \pi \cdot 392\text{cm}^3$

$V = 392\pi \text{ cm}^3$

Compare your answer with the correct one above

Tap the card to reveal the answer