Question

3) An open top box is to be constructed out of a 90 inch by 70 inch piece of cardboard by cutting squares out of the corners and then folding the side flaps up. If the squares all have sides of 15 inches, find the following.

a) Volume in cubic inches.
b) Volume in cubic feet.
c) Volume in cubic yards.

Answer 1

a) The volume in cubic inches is 36000

b) The volume in cubic feet is 125/6

c) The volume in cubic yard is 125/162

Explanation:

* Lets study the information of the problem to solve it

- The dimensions of the piece of cardboard are 90 inches by 70 inches

- The side of the cutting square is 15 inches

- The squares are cutting from each corner

∴ Each dimension of the cardboard will decrease by 2 × 15 inches

∴ The new dimensions of the piece of cardboard are;

90 - (15 × 2) = 90 - 30 = 60 inches

70 - (2 × 15) = 70 - 30 = 40 inches

- The dimensions of the box will be:

# Length = 60 inches

# width = 40 inches

# height = 15 inches

- The volume of any box with three different dimensions is

V = Length × width × height

∵ The length = 60 inches

∵ The width = 40 inches

∵ The height = 15 inches

∴ V = 60 × 40 × 15 = 36000 inches³

a) The volume in cubic inches is 36000

* Now lets revise how to change from inch to feet

- 1 foot = 12 inches

∵ 1 foot = 12 inches

∴ 1 foot³ = (12)³ inches³

∴ 1 foot³ = 1728 inches³

∵ The volume of the box is 36000 inches³

∴ The volume of the box in cubic feet = 36000 ÷ 1728 = 125/6

b) The volume in cubic feet is 125/6

* Now lets revise how to change from feet to yard

- 1 yard = 3 feet

∵ 1 yard = 3 feet

∴ 1 yard³ = (3)³ feet³

∴ 1 yard³ = 27 feet³

∵ The volume of the box is 125/6 feet³

∴ The volume of the box in cubic yard = 125/6 ÷ 27 = 125/162

c) The volume in cubic yard is 125/162

Answer 2

3600 cubic inches , 2.08 cubic feet , 0.0771 cubic yards

Explanation:

Here we are given that the open box has been constructed from a card board with length 90 inches and width 70 inches by

1. cutting a square card board

2. of each side 15 inches

Hence when we are done with folding it for our cuboid , we find our new

1. Length = 90-15-15 = 60 inches

2. width = 70-15-15 = 40 inches

3. Height = 15 inches

Now we know the volume of any cuboid is given as

V= Length * width * height

= 60*40*15

= 3600 cubic inches

Part 2 . Now let us convert them into cubic feet

1 cubic inch = 0.000578704 cubic feet

Hence 3600 cubic inches = 3600 * 0.000578704 cubic feet

=2.083 cubic feet

Part 3. Now let us convert them into cubic yards

1 cubic inch = 0.0000214335 cubic yards

Hence 3600 cubic inches = 3600 * 0.0000214335 cubic yards

= 0.0771 cubic yards