Question

A candy bar box is in the shape of a triangular prism. The volume of the box is 3,240 cubic centimeters. A triangular prism is shown with base of triangle labeled 24 cm, sides of the triangle labeled 15 cm, and length of the box equal to 30 cm. Part A: What is the height of the box? Show your work. (5 points) Part B: What is the approximate amount of cardboard used to make this candy box? Explain how you got your answer.

Answer 1

Part A:

We all know the formula for solving the volume of a triangular prism, which is V = ½ (b · h · l). Using this formula, we can solve h, the height of the base, with the given information.

3,240 = ½(24 · h·  30)

3,240 = ½(24 · 30 · h)

3,240 = ½(720 · h)

3,240 = (½ · 720)h

3,240 = 360h

3,240 ÷ 360 = 360h ÷ 360

9 = h

So, the height of the base is 9 centimeters.

Part B:  

There are two triangular faces, each with a base of 24 centimeters and a height of 9 centimeters. Using the formula A = ½ (b · h), we can calculate the area of each face, which is:

½ (24 · 9) = 108 sq cm.  

Because we have two of them, we will multiply the answer by two.  

108(2) = 216 sq cm

There are two rectangular faces whose dimensions are 15 cm by 30cm; Using the formula A = b · h, we can calculate the area of each face, which is:

15 · 30 = 450.  

Because we have two of them, we will multiply the answer by two.

450(2) = 900 sq cm.

There is one rectangular face whose dimensions are 30 cm by 24 cm. There is one rectangular face whose dimensions are 30 cm by 24 cm. Using the same formula as before, we can calculate the area which is:

30 · 24 = 720 sq cm.

This makes the total surface area

216 + 900 + 720 = 1,836 sq cm.

So the surface area of the triangular prism is 1,836 sq cm.

Answer 2

Answer:

Part A - 9 cm; Part B - 1836 cm²

Step-by-step explanation:

Part A:  The volume of a triangular prism is given by the area of the base (area of the triangle) multiplied by the length of the box.  To find the area of a triangle, we use the formula A = 1/2bh; this gives us

V = 1/2bhl

Using the information we have gives us

3240 = 1/2(24)(h)(30)

3240 = 360h

Divide both sides by 360:

3240/360 = 360h/360

9 = h

Part B:  We are looking for the surface area of this prism.

There are two triangular sides, each with a base of 24 and a height of 9.  Their areas are:

A = 1/2bh = 1/2(24)(9) = 108 sq cm each.  For two of them, this makes

108(2) = 216 sq cm

There are two rectangular sides whose dimensions are 15 by 30; their areas are

A = 15(30) = 450.  For two of them, this makes

450(2) = 900 sq cm.

There is one rectangular side whose dimensions are 30 by 24.  Its area is

A = 30(24) = 720 sq cm.

This makes the total surface area

216+900+720 = 1836 sq cm.