Question

A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles?

Answer 1

it is 27 π cubic inches

Answer 2

The amount of wax that is needed to create one set of candles is:

27π cubic inches.

Explanation:

• The radius(r) of the smallest candle=0.5 inches.

Height(h) of smallest candle= 3 inches.

Hence, Volume of smallest candle
`V_1` is:

`V_1=\pi r^2h`

• Now the medium candle is one which is obtained by taking a scale factor of 2.

Hence, radius of medium candle=2r

Height of medium candle=2h

Hence, Volume of medium candle
`V_2` is:

`V_2=\pi* (2r)^2* (2h)\\\\V_2=8\pi r^2h`

• Similarly the largest candle is one which is obtained by taking a scale factor of 3.

Hence, radius of largest candle=3r

Height of largest candle=3h

Hence, Volume of largest candle
`V_3` is:

`V_3=\pi* (3r)^2* (3h)\\\\V_3=27\pi r^2h`

The amount of wax required to create one set of candle is equal to total volume of all the three candles.

`\text{Amount\ of\ wax}=V_1+V_2+V_3\\\\\\\text{Amount\ of\ wax}=\pi r^2h+8 \pi r^2h+27\pi r^2 h\\\\\\\text{Amount\ of\ wax}=36\pi r^2h`

Now on putting the value of r and h in the expression we get:

`\text{Amount\ of\ wax}=36* \pi* (0.5)^2* 3\\\\\\\text{Amount\ of\ wax}=27\pi\ \text{cubic\ inches}`

Hence, the answer is:

27π cubic inches.