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: Recall volume formula for prism

The volume formula for a triangular - prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height of the prism. We know $V = 270$ cm³ and $h=18$ cm. First, find the area of the base.
$B=\frac{V}{h}=\frac{270}{18}=15$ cm².

Step2: Find the height of the triangular base

The area of a triangle is $B=\frac{1}{2}bh$, where $b = 5$ cm is the base of the triangle. We know $B = 15$ cm². Solving for the height of the triangle $h_{triangle}$:
$15=\frac{1}{2}\times5\times h_{triangle}$, then $h_{triangle}=\frac{15\times2}{5}=6$ cm.

Step3: Determine box dimensions

To fit the oblique triangular - shaped candle, the box dimensions should be the maximum lengths in each direction. The height of the candle is 18 cm, the slanted width of the candle is 7 cm, and the height of the triangular base is 6 cm. So the box dimensions are 7 cm by 6 cm by 18 cm.

Answer:

7 cm by 6 cm by 18 cm