Question

The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant. The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters. A second prism has a length of 12 centimeters and a width of 8 centimeters. What is the volume of the second prism? 576 cubic centimeters 768 cubic centimeters 784 cubic centimeters 1,344 cubic centimeters

Answer 1

The correct option is 1.

Explanation:

The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant.

Let the height of both rectangular prism be h cm.

The volume of a prism is

`V=l* b* h`

Where, l is length, b is breadth or width and h is height.

The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters.

`672=8* 14* h`

`672=112h`

Divide both sides by 112.

`(672)/(112)=h`

`6=h`

The value of h is 6 cm. It means the height of both prism is 6 cm.

A second prism has a length of 12 centimeters and a width of 8 centimeters. So, the volume of second prism is

`V=12 * 8* 6`

`V=576`

The volume of second prism is 576 cubic centimeters. Therefore the correct option is 1.

Answer 2

1st Prism = 8*14 = 112

672/112 = 6

2nd prism = 8*12=96

96*6 = 576 cubic cm

answer is 576 cubic centimeters