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

Answer:

The correct option is 1.

Step-by-step 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

$V=l\times b\times h$

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.

$672=8\times 14\times h$

$672=112h$

Divide both sides by 112.

$\frac{672}{112}=h$

$6=h$

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

$V=12 \times 8\times 6$

$V=576$

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