Question

The volume of a rectangular prism is 2,058 cubic cm. The length of the prism is 3 times the width. The height is twice the width.

Answer 1

Solution:

We have:
length = a = 3x
width = b = x
height = h = 2x
area of the base of the prism = c 
volume of the prism = v = 2058 cm³

Use: c = (3x)(x)
c = 3x² 

Use: v = (3x²)(2x)
v = 6x³
2058 = 6x³
6x³ = 2058
x³ = 2058 / 6
x³ = 343
x = ∛343
x = 7

a = 3x
a = 3(7)
a = 21 

b = x 
b = 7

h = 2x
h = 2(7)
h = 14

c = 3x²
c = 3(7)²
c = 3(49)
c = 147

a = 21 cm
b = 7 cm
h = 14 cm
c = 147 cm²