Question

A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.

A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 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 the sides of the candy box? Explain how you got your answer. (5 points)

Answer 1

A) 12 cm

B) 520 cm² (just sides); 720 cm² (sides and base)

Explanation:

A)

The volume of a triangular prism is given by the formula ...

V = 1/2LWH . . . L = length, W = width, H = height

Filling in the given dimensions, we can find the height.

1200 cm³ = 1/2(20 cm)(10 cm)H

1200 cm³/(100 cm²) = H = 12 cm . . . . divide by the coefficient of H

The height of the box is 12 cm.

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B)

Only the two rectangular faces with dimensions 13 cm by 20 cm are described in this problem statement as "sides." The area of each of those two faces is ...

A = LW

A = (20 cm)(13 cm) = 260 cm²

So, the area of the two sides is ...

2 × 260 cm² = 520 cm² . . . . area of sides

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If we also describe the base as a side of the box, its area is ...

A = LW = (20 cm)(10 cm) = 200 cm²

Added to the area of the other two sides, the total "side" area is 720 cm².