Question

an oblique candle with a volume of 270 cubic centimeters is 18 centimeters tall. the width of the triangular candle base is 5 centimeters, and the width of the slanted candle is 7 centimeters. what dimensions of the box are required to fit the candle? 5 cm by 6 cm by 18 cm 7 cm by 6 cm by 18 cm 5 cm by 3 cm by 18 cm 7 cm by 3 cm by 18 cm

Explanation:

Step1: Find the area of the triangular base

The volume formula for a triangular prism (the candle) is \(V = Bh\), where \(B\) is the area of the base and \(h\) is the height. Given \(V = 270\space cm^{3}\) and \(h=18\space cm\). Then \(B=\frac{V}{h}\).

$$B=\frac{270}{18}=15\space cm^{2}$$

Step2: Find the height of the triangular base

The area formula for a triangle is \(B=\frac{1}{2}bh\), where \(b = 5\space cm\) (base of the triangle) and \(B = 15\space cm^{2}\). Then \(\frac{1}{2}\times5\times h_{triangle}=15\). Solving for \(h_{triangle}\):

$$h_{triangle}=\frac{15\times2}{5}=6\space cm$$

Answer:

5 cm by 6 cm by 18 cm