Find the weight of a right rectangular prism with length 13 ft, width 6 ft, and height 2.5 ft if the contents weigh 0.02 pounds per cubic inch.
I think it's 31.2 but I'm having doubts. Can you help me?
The volume is 13 x 6 x 2.5 cubic feet
= 195 cubic feet
1 cubic foot = 1728 cubic inches, so..
your volume is 336960 cubic inches, which at .02 lbs per cubic inch
= 6739.2 lbs
To find the weight of a right rectangular prism, you need to calculate the volume of the prism and then multiply it by the weight per cubic unit.
First, calculate the volume of the prism using the formula:
Volume = length * width * height
Given:
Length = 13 ft
Width = 6 ft
Height = 2.5 ft
Volume = 13 ft * 6 ft * 2.5 ft = 195 ft³
Next, convert the volume to cubic inches since the weight is given in pounds per cubic inch. Note that 1 cubic foot is equal to 12^3 = 1728 cubic inches.
Volume (in cubic inches) = 195 ft³ * 1728 in³/ft³ ≈ 336,960 in³
Now, multiply the volume (in cubic inches) by the weight per cubic inch to get the weight of the prism:
Weight = Volume * Weight per cubic inch
Given:
Weight per cubic inch = 0.02 pounds/in³
Weight = 336,960 in³ * 0.02 lb/in³ ≈ 6,739.2 lbs
So, the weight of the right rectangular prism is approximately 6,739.2 pounds.
Therefore, your initial estimate of 31.2 is incorrect.