Question

A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters.

Answer 1

Answer:

Part A) The height of the base is 15 cm

Part B) $SA=1,240\ cm^2$

Step-by-step explanation:

Part A)  What is the height of the base?

we know that

The volume of the triangular prism is equal to

$V=BL$

where

B is the area of the triangular face

L is the length of the prism

we have

$V=2,400\ cm^3\\L=20\ cm$

substitute the given values

$2,400=B(20)$

solve for B

$B=2,400/20\\B=120\ cm^2$

Find the height of the base

we know that

The area of triangle i equal to

$120=\frac{1}{2}(16)h$

solve for h

$h=240/16\\h=15\ cm$

Part B) What is the approximate amount of cardboard used to make the candy box?

we know that

To find out the the approximate amount of cardboard used to make the candy box, determine the surface area of the triangular prism

The surface area is equal to

$SA=2B+PL$

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length

we have

$B=120\ cm^2\\L=20\ cm$

Find the perimeter of triangle P

$P=17+17+16=50\ cm$

substitute

$SA=2(120)+50(20)=1,240\ cm^2$