Question

The expression V = 2x3 + 6x2 can be used to find the volume of the trapezoidal prism below.

A trapezoidal prism is shown. The bases of the trapezoid have lengths of x + 2 and x + 4. The height of the trapezoid is x. The height of the prism is 2 x.
If x = 12 cm, what is the volume of the prism?

Answer 1

4320

Explanation:

V = 2x^3 + 6x^2

x = 12

V = 2(12^3) + 6(12^2)

V = 2(1728) + 6(144)

V = 3456 + 864

V = 4320

Answer 2

• 4320 cm³

Explanation:

Volume formula for prism:

• V = Ah, where A- area of bas, h- height of base

Area of base:

• A = 1/2(b1 + b2)h = 1/2(x + 2 + x + 4)x = 1/2(2x + 6)x = x(x+3)

Volume of prism is:

• V = 2x*x(x + 3) = 2x³ + 6x²

If x = 12, then the value of V is:

• V = 2*12³ + 6*12² = 4320 cm³