Question 4 (Essay Worth 10 points) (05.05 HC)

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)

Step-by-step explanation:

Find the height using Pythagoras.

height = sqrt(hypotenuse^2 - (1/2*base^2) )

height = sqrt(15^2 - (1/2 * 24)^2  )

height = sqrt(225 - 12^2)

height = sqrt(225 - 144)

height = sqrt(81)

height = 9

Two sides

Area one side = L*W

Area one side = 30 * 15

Area one side = 450 cm^2

Area of both sides =                                          900 cm^2

Triangular base

Area one triangle = 1/2 * base * height

Area one  triangle = 1/2 * 24 * 9

Area one triangle = 12 * 9

Area one triangle = 108

Area both triangles =                                         216 cm^2

Flat bottom

Area = L * W

Area = 30 * 24

Area =                                                                720 cm^2

Total amount needed                                       1836 cm^2

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."