Question

A candy bar box is in the shape of a triangular prism. The volume of the box is 3,240 cubic centimeters Part A: What is the height of the base? Show your work. (5 points) Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)

Answer 1

Answer:

a) Height of the base of the prism = 9 cm

b) The amount of cardboard required to make the candy box = 1,836 cm² area.

Step-by-step explanation:

For any prism, the volume is given as area of two opposing faces multuplied by the perpendicular distance between the two faces.

For this triangular prism, the base of the prism will be the two opposite faces separated by a perpendicular distance.

Hence, the base of this prism is its triangular face.

We can use either Pythagoras theorem (since the triangle is made up of two right angle triangles) or the formula for the volume of the prism to compute this height.

Using Pythagoras theorem

(Hyp)² = (Adj)² + (Opp)²

Hyp = 15 cm

Adj = Height

Opp = (24/2) = 12 cm

15² = (Height)² + 12²

(Height)² = 225 - 144 = 81

Height = 9 cm

OR

Volume of a prism = (Base area) × (Perpendicular height)

Volume = 3240 cm³

Perpendicular height = 30 cm

Base area = Area of triangular face = ½ × (base) × (Height)

Base = 24 cm

Height = H = ?

3240 = (½×24×H) × 30

3240 = 360H

H = (3240/360) = 9 cm

b) To obtain the cardboard that will be required, we need to calculate the total surface area of the prism

The prism consists of two identical triangular faces and 3 rectangular faces (2 identical rectangular faces and another)

Area of a triangle = ½bh

Area of a rectangle = Length × Breadth

Total surface area of the prism = (½×24×9) + (½×24×9) + (30×15) + (30×15) + (30×24)

= 1,836 cm²

Hope this Helps!!!