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 volume of the second rectangular  prism is  576 cm³ .

Step-by-step explanation:

As given

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

Let us assume that the length is denoted by L .

Let us assume that the Breadth is denoted by B.

Thus

$V \propto L\times B$

V = L × B ×  H

where H is the constant of variation

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

Volume (V) = 672 cm

Length (L) = 8 cm

Width (B) = 14 cm

Put all the values in the above

672 = 8 × 14 ×  H

672 = 112H

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

H = 6

As given

A second prism has a length of 12 centimeters and a width of 8 centimeters.

Length = 12 cm

Width =  8 cm

Height = 6cm

Put all the values in V = L × B ×  H .

V = 12 × 8  ×  6

V = 576 cm³

Therefore the volume of the second rectangular  prism is  576 cm³ .

Answer 2

The volume of the second prism is 576 cubic centimeters. Since both prisms have the same height, I solved for the height using the data given with the first prism (I got 6 centimeters for the height). And then I calculated for the volume of the second prism.