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

Answer:

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

                              27π cubic inches.

Step-by-step 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:

       $V_2=\pi\times (2r)^2\times (2h)\\\\V_2=8\pi r^2h$

• 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:

       $V_3=\pi\times (3r)^2\times (3h)\\\\V_3=27\pi r^2h$

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:

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

                  Hence, the answer is:

                       27π cubic inches.