# Volume and Surface Area of a Cylinder - ACT Math

Quesbook
QOTD
Apr 20th 2017

Finding the volume and surface area of a cylinder (3-D geometry) is a skill tested on ACT Math. Check out its definition, formulas, and example questions.

A cylinder is a tube, where the 2 flat ends are circles.

## Surface Area of a Cylinder

To calculate the surface area of a cylinder you must know the radius of the circle (r) which makes up the flat side, as well as how far the cylinder extends to the other flat side, this is defined as the height (h). The equation is:

Surface Area = $$2\pi\;rh\;+\;2\pi\;r^{2}$$

## Volume of a Cylinder

To calculate the volume of a cylinder you are finding the amount of space inside of the cylinder. The equation is:

Volume = $$\pi\;r^{2}\;h$$

## Practice Questions

Question 1

To make a cylindrical, non-tapering pail using a tin sheet, Tony needs to determine the area of the sheet to be used. The pail's height will be 40 cm; and its radius will be 5 cm. If the pail has no cover, approximately how many square centimeters of tin sheet will Tony need to make this pail?

A. 400π
B. 425π
C. 450π
D. 500π
E. 1,000π

Explanation

The answer is B. The area of the cylindrical side of the pail is π(2×5)(40)=400π. The area of the pail bottom is π(5)2=25π. Therefore the total area of tin sheet needed is 400π+25π=425π

Question 2

The volume, V, of a right circular cylinder with radius r and height h is given by the formula $$V=\pi r^{2}h$$. The first right circular cylinder has radius 2R and height 4H. A second right circular cylinder has radius 16R and height 8H. The volume of the second right circular cylinder is how many times the volume of the first right circular cylinder?

A. 2
B. 8
C. 16
D. 64
E. 128

Explanation

The answer is E. The volume of the first cylinder is: $$V_1=\pi (2R)^{2}(4H)=16\pi R^{2}H$$   The volume of the second cylinder is: $$V_2=\pi (16R)^{2}(8H)=2048\pi R^{2}H$$   The ratio of the two volumes is: $$\dfrac{V_2}{V_1}=\dfrac{2048\pi R^{2}H}{16\pi R^{2}H}=\dfrac{2048}{16}$$=$$128$$

Check out other geometry formulas for 3-D objects