Question

Which rectangular prism has a surface area of 56 square units? [Note: Art is not drawn to scale.] A rectangular prism with a length of 5, width of 3, and height of 1. A rectangular prism with a length of 2, width of 2, and height of 6. A rectangular prism with a length of 5, width of 3, and height of 2. A rectangular prism with a length of 6, width of 2, and height of 4.

Answer 1

the answer is c

Explanation:

Answer 2

The rectangular prism with a length of 2, width of 2, and height of 6 has a surface area of 56 sq. units.

Explanation:

The surface area of a rectangular prism is equal to the sum of the three lateral surfaces, multyplied then by a factor of 2. One surface is the product of the length and the width, the other is the product of the length and the height, and the last is the product of the width and the height.

If l: length, w: width and h: height, we can express the surface area as:

`S=2(lw+lh+wh)`

A rectangular prism with a length of 5, width of 3, and height of 1.

`S=2(lw+lh+wh)=2*(5\cdot3+5\cdot1+3\cdot1)=2*(15+5+3)=2*23\\\\S=46`

A rectangular prism with a length of 2, width of 2, and height of 6.

`S=2(lw+lh+wh)=2*(2\cdot2+2\cdot6+2\cdot6)=2*(4+12+12)=2*28\\\\S=56`

A rectangular prism with a length of 5, width of 3, and height of 2.

`S=2(lw+lh+wh)=2*(5\cdot3+5\cdot2+3\cdot2)=2*(15+10+6)=2*31\\\\S=62`

A rectangular prism with a length of 6, width of 2, and height of 4.

`S=2(lw+lh+wh)=2*(6\cdot2+6\cdot4+2\cdot4)=2*(12+24+8)=2*44\\\\S=88`