Finding the volume of a rectangular prism:

Question

A rectangular prism has a square base and it’s length is double the height or width. If the surface area of all six sides are equal to 250ft^2. Then what is the volume of this object?

Answer 1

l = length, w = width, h = height

From description, l = 2h = 2w

Since it has a square base,w=h

V = lwh = 2w•w•w = 2w³

Surface area, A = 2(wl+hl+hw) = 2(2w²+2w²+w²) = 250

5w²=250/2 = 125

w²= 25

w = √25 = 5 (positive value since it is a width)

V= 2(5)³ = 2(125)= 250 ft²

Answer 2

S = 2 w^2 + 4wl = 2w^2 + 4w(2w) = 10w^2

10w^2 = 250

w^2 = 25

w = 5

h = 5

l = 10

V = lwh = 5*5*10 = 250 ft^3

Answer 3

Draw and label a diagram!

SA = 2x² + 4(x)(2x)

SA = 2x² + 8x²

SA = 10x²

250 = 10x²

25 = x²

5 = x

Can you now calculate the volume?