This handy **Spectrum Math Grade 7 Answer Key Chapter 5 Lesson 5.11 Volume: Rectangular Prisms** provides detailed answers for the workbook questions

## Spectrum Math Grade 7 Chapter 5 Lesson 5.11 Volume: Rectangular Prisms Answers Key

Volume is the amount of space a solid (three-dimensional) figure occupies. You can calculate the volume of a rectangular solid by multiplying the area of its base by its height: V = Bh.

The area of the base is found by multiplying length and width. B = l × w, so the volume can be found by using the formula V = l × w × h.

If l = 10 m, w = 11 m, and h = 7 m, what is the volume of the solid?

V = 10 × 11 × 7 V = 770 m^{3} or 770 cubic meters.

Because the measure is in 3 dimensions, it is measured in cubic units or units^{3}.

**Find the volume of each rectangular solid.**

Question 1.

a.

V = _____________ cm^{3}

Answer:

V = 2,340 cm^{3}

Explanation:

V = l × w × h.

l = 12 cm, w = 15 cm, and h = 13 cm,

V = 12 × 15 × 13

V = 180 x 13

V = 2,340 cm^{3}

b.

V = ______________ mm^{3}

Answer:

V = 3,600 mm^{3}

Explanation:

V = l × w × h.

l = 20 mm, w = 18 mm, and h = 10 mm,

V = 20 × 18 × 10

V = 360 x 10

V = 3,600 mm^{3}

c.

V = ______________ cm^{3}

Answer:

V = 968 cm^{3}

Explanation:

V = l × w × h.

l = 8 cm, w = 11 cm, and h = 11 cm,

V = 8 × 11 × 11

V = 88 x 11

V = 968 cm^{3}

Question 2.

a.

V = ______________ ft.^{3}

Answer:

V = 300 ft^{3}

Explanation:

V = l × w × h.

l = 5 ft, w = 8 ft, and h = 7.5 ft,

V = 5 × 8 × 7.5

V = 40 x 7.5

V = 300 ft^{3}

b.

V = ______________ in.^{3}

Answer:

V = 324 in^{3}

Explanation:

V = l × w × h.

l = 6 in, w = 6 in, and h = 9 in,

V = 6 × 6 × 9

V = 36 x 9

V = 324 in^{3}

c.

V = ______________ ft.^{3}

Answer:

V = 1,728 ft^{3}

Explanation:

V = l × w × h.

l = 12 ft, w = 12 ft, and h = 12 ft,

V = 12 × 12 × 12

V = 144 x 12

V = 1,728 ft^{3}

Question 3.

a.

V = _______________ m^{3}

Answer:

V = 1,056 m^{3}

Explanation:

V = l × w × h.

l = 8 m, w = 12 m, and h = 11 m,

V = 8 × 12 × 11

V = 96 x 11

V = 1,056 m^{3}

b.

V = _______________ in.^{3}

Answer:

V = 648 in^{3}

Explanation:

V = l × w × h.

l = 6 in, w = 9 in, and h = 12 in,

V = 6 × 9 × 12

V = 54 x 12

V = 648 in^{3}

c.

V = ________________ m^{3}

Answer:

V = 375 m^{3}

Explanation:

V = l × w × h.

l = 5 m, w = 15 m, and h = 5 m,

V = 5 × 15 × 5

V = 75 x 5

V = 375 m^{3}