Mathematics, 19.04.2021 21:10 via21

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

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

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Answer from: depression4eternity

Part A:

15 cm

Part B:

1240cm^2

Step-by-step explanation:

Part A:

Given the volume of the box, along with the base and length, we can calculate the value of the height using the following formula:

$V = \frac{1}{2} bhl=2400\\b = Base=16\\h = Height = ?\\l=Length =20$

Substitute the values into the equation:

2400 = $\frac{1}{2}$ × 16 × h × 20

Multiply

2400 = 160h

Divide both sides by 160 to isolate the variable.

15 = h

Part B:

The amount of cardboard used is the surface area.

There are two methods to calculate the surface area:

1) First method:

A = bh + l(s1+s2+s3)

s: The sides of the Triangle/Base. (16, 17, 17)

Substituting the numbers into the equation you get:

A = 16×15 + 20(16+17+17)

A = 240 + 20(50)

A = 240 + 1000

A = 1240cm^2

2) Second method:

Calculate all sides individually to get the sum.

A = 2( 20 × 17 ) + 2( $\frac{1}{2}$ × 16 × 15 ) + ( 16 × 20 )

A = 2(340) + 2(120) + 320

A = 680 + 240 + 320 = 1240cm^2

The values in the brackets are the formulas for the area of each side.

We multiply the formulas by the number of matching sides.

(i.e There are 2 rectangular sides with the measurements 17 and 20)

Answer from: Quest

step-by-step explanation:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since 2010 0 1 2 3 4 5

profits made in 1000's 39 84 111 120 111 84

we find that profit gradually increases form 2010 to 2013 upto 120, then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

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