Question

Margaret wants to cover a footrest in the shape of a rectangular prism with cotton fabric. The footrest is 18 in. 12 in. 10 in. She has 1 yd2 of fabric. Can she completely cover the footrest?

Answer 1

The surface area of the footrest is 1032In²

And since she has 1yd²(1296in²) of fabric she cannot cover the footrest completely

Explanation:

Kindly find attached rough sketch of the rectangular prism for your reference.

This problem bothers on the mensuration of solid shapes, a rectangular prism

To solve the problem we need to calculate the total surface area of the prism and compare it with her 1yd fabric

Given data

Length 18 in.

Width 12 in.

Height 10 in

SA=2(wl+hl+hw)

SA= 2(12*18+ 10*18+ 10*12)

SA= 2(216+180+120)

SA= 2(516)

SA= 1032In²

Let us make the comparison

1 yd² is equal to 1296in²

Answer 2

No, she cannot completely cover the footrest.

Explanation:

First of all, we need to find the total surface area of the prism to be covered using the cotton cloth

the total surface area of the prism is

A = 2wl + 2lh + 2hw,

l is the length of the prism = 18 in,

w= width of the prism = 12 in,

h is the height of the prism = 10 in

hence
`A = 2(12 * 18 ) + 2(18 * 10) + 2(10 * 12)=1032in^(2)`

We need to convert the area of the fabric to be in the same unit as that of the prism

Area of cotton fabric =
`1 yd^(2)= 1296 in ^(2)`

since the surface area of the foot rest is more than the area of fabric she has, she cannot completely cover the footrest