Question

a factory makes candles. each candle is in the shape of a triangular prism, as shown below. if the factory made 16 such candles, how much wax did the factory use (in cubic centimeters)?

Explanation:

Step1: Calculate the area of the triangular base

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(4\) cm and the height is \(6\) cm. So, \(A = \frac{1}{2}\times4\times6= 12\) \(cm^{2}\).

Step2: Calculate the volume of one triangular - prism - shaped candle

The formula for the volume of a prism is \(V=A\times length\), where \(A\) is the area of the base and \(length\) is the length of the prism. The length of the prism (candle) is \(8\) cm. So, \(V = 12\times8=96\) \(cm^{3}\).

Step3: Calculate the total volume for 16 candles

If one candle has a volume of \(96\) \(cm^{3}\), then for \(16\) candles, the total volume \(V_{total}=96\times16 = 1536\) \(cm^{3}\).

Answer:

\(1536\) \(cm^{3}\)