Q:

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.

Accepted Solution

A:
Answer: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 Step-by-step 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