Question

A candlemaker uses 240 cubic centimeters of wax to create a scented candle using a cylindrical mold. He decides to offer a larger-sized candle, which uses twice as much wax as the smaller-sized candle.

Which mold can he use to make the larger-sized candle?

A. a cylinder with a height that is the same as the height of the original mold, and a radius that is double the radius of the original mold

B. a cylinder with a height that is double the height of the original mold, and a radius that is one-half the radius of the original mold

C. a cylinder with a height and a radius that are each double the length of those of the original mold

D. a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold

Answer 1

D. a cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold

Explanation:

You want to know possible changes to radius and height that will double the volume of a cylinder.

Volume

The volume of a cylinder is given by the formula ...

V = πr²h

This tells you the volume is proportional to the height, and proportional to the square of the radius.

Double volume

This proportionality tells you that the volume can be doubled by ...

• using the same height, and doubling the square of the radius
• using the same radius, and doubling the height.

We note that doubling the radius will multiply the square of the radius by 4:

R = 2r

R² = (2r)² = 4(r²)

The second option above (double height only) matches choice D.

<95141404393>