an oblique candle with a volume of 270 cubic centimeters is 18 centimeters tall. the width of the triangular…

Explanation:

Step1: Find the area of the base of the candle

The volume formula for a prism is $V = Bh$ (where $V$ is volume, $B$ is the area of the base, and $h$ is height). Given $V = 270$ cubic - cm and $h = 18$ cm. We can find $B$ by rearranging the formula: $B=\frac{V}{h}$. So, $B=\frac{270}{18}=15$ square - cm.

Step2: Find the height of the triangular base

The base of the candle is a triangle. The area formula for a triangle is $B=\frac{1}{2}bh$ (where $b$ is the base of the triangle and $h$ is the height of the triangle). Given $b = 5$ cm and $B = 15$ square - cm. We can find the height of the triangle by rearranging the formula: $h=\frac{2B}{b}$. So, $h=\frac{2\times15}{5}=6$ cm.

Step3: Determine the dimensions of the box

The box needs to fit the candle. The height of the box will be the same as the height of the candle, which is 18 cm. The base of the box should be large enough to fit the base of the candle. The base of the candle has a base length of 5 cm and a height of 6 cm for the triangular base, and the slant - width of the candle is 7 cm. The dimensions of the box should be 5 cm (base length of the triangle) by 6 cm (height of the triangle) by 18 cm (height of the candle).

Answer:

5 cm by 6 cm by 18 cm