Question

Which figure has a greater volume and by how much?

The volume of figure 1 is 45 centimeters cubed greater than the volume of figure 2.
The volume of figure 2 is 45 centimeters cubed greater than the volume of figure 1.
The volume of figure 1 is 120 centimeters cubed greater than the volume of figure 2.
The volume of figure 2 is 120 centimeters cubed greater than the volume of figure 1.

Answer 1

A) The volume of figure 1 is 45 cm³ greater than the volume of figure 2

Explanation:

Answer 2

A) The volume of figure 1 is 45 cm³ greater than the volume of figure 2

Explanation:

Let's start by calculating the volumes of both figures

Figure 1

Rectangular prism

V = Bh

V = (15*6)(5)

V = (90)(5)

V = 450 cm³

Triangular prism

V = Bh

V = 1/2(3*15)(6)

V = 1/2(45)(6)

V = 1/2(270)

V = 135 cm³

Add them together, you get 585 cm³

Figure 2

Rectangular prism

V = Bh

V = (6*15)(5)

V = (90)(5)

V = 450 cm³

Rectangular pyramid

V = 1/3 Bh

V = 1/3 (15*6)(3)

V = 1/3 (90)(3)

V = 1/3 (270)

V = 90 cm³

Add them together, you get 540 cm³

Subtract 540 from 585 and get 45