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.
