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.

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 = \(2\pi\;rh\;+\;2\pi\;r^{2}\)

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

Volume = \(\pi\;r^{2}\;h\)

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

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

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

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**