We included **HMH Into Math Grade 7 Answer Key PDF** **Module 11 Analyze Surface Area and Volume **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 11 Answer Key Analyze Surface Area and Volume

**The Prism Family**

Each of the rectangular prisms shown is made from cubes with an edge length of 1 centimeter. All of the prisms in this family have something in common.

Investigate by finding the dimensions, surface area, and volume of each prism. How are they all related?

A.

Dimensions: _____________, ___________, ___________

Surface area: _____________

Volume: _____________

Answer:

Dimensions: 2cm, 6cm, 2cm

Surface area: 56 cm^{2}

Volume: 24 cm^{3}

Explanation:

Dimensions: *l* = 2cm, w = 6cm, h = 2cm

Surface area: A

A = 2(*l *x w + w x h x h x *l*)

A = 2(6×2 + 2×2 + 2×6)

A = 2(12 + 4 + 12)

A = 2(28)

A = 56 cm^{2}

Volume: V = (*l*).(w).(h)

V = 2 x 6 x 2 = 24 cm^{3}

B.

Dimensions: _____________, ___________, ___________

Surface area: _____________

Volume: _____________

Answer:

Dimensions: 4cm, 2cm, 3cm

Surface area: 52 cm^{2}

Volume: 24 cm^{3}

Explanation:

Dimensions: *l* = 4cm, w = 2cm, h = 3cm

Surface area: A

A = 2(*l *x w + w x h x h x *l*)

A = 2(4×2 + 2×3 + 3×4)

A = 2(8 + 6 + 12)

A = 2(26)

A = 52 cm^{2}

Volume: V = (*l*).(w).(h)

V = 4 x 2 x 3 = 24 cm^{3}

C.

Dimensions: _____________, ___________, ___________

Surface area: _____________

Volume: _____________

Answer:

Dimensions: 8cm, 3cm, 1cm

Surface area: 70 cm^{2}

Volume: 24 cm^{3
}Explanation:

Dimensions: *l* = 8cm, w = 3cm, h = 1cm

Surface area: A

A = 2(*l *x w + w x h x h x *l*)

A = 2(8×3 + 3×1 + 1×8)

A = 2(24 + 3 + 8)

A = 2(35)

A = 70 cm^{2}

Volume: V = (*l*).(w).(h)

V = 8 x 3 x 1 = 24 cm^{3}

**Turn and Talk**

Describe the family of rectangular prisms.

Answer:

A rectangular prism is a three-dimensional shape, having six faces,

where all the faces (top, bottom, and lateral faces) of the prism are rectangles. Cuboids, Rectangular Prisms and Cubes.

**Are You Ready?**

Complete these problems to review prior concepts and skills you will need for this module.

**Explore Volume**

Each rectangular prism is composed of cubes with an edge length of 1 inch. Determine the volume of each prism.

Question 1.

__________ in^{3}

Answer:

16 cm^{3}

Explanation:

Volume: V = (*l*).(w).(h)

V = 4 x 2 x 2 = 16 cm^{3}

Question 2.

__________ in^{3}

Answer:

18 cm^{3}

Explanation:

Volume: V = (*l*).(w).(h)

V = 2 x 3 x 3 = 18 cm^{3}

**Nets and Surface Area**

**Draw a net of each prism. Then use the net to determine the surface area of the prism.**

Question 3.

____________ cm^{2}

Answer:

A = 62 cm^{2
}Explanation:

Dimensions: *l* = 5cm, w = 2cm, h = 3cm

Surface area: A

A = 2(*l *x w + w x h x h x *l*)

A = 2(5×2 + 3×2 + 3×5)

A = 2(10 + 6 + 15)

A = 2(31)

A = 62 cm^{2}

Question 4.

____________ m^{2}

Answer:

A = 168 m^{2
}Explanation:

A = 2(*l *x w + w x h x h x *l*)

A = (6×5 + 5×8 +10×5) + 6×8

A = 30 + 40 + 50 + 48

A = 168 m^{2}

**Cross Sections of Circular Solids**

Question 5.

Answer:

There are two different types of the cross-section.

1. Horizontal or parallel cross-section.

2. Vertical or perpendicular cross-section.

Explanation:

Horizontal cross-section:

A plane cuts the solid shape in the horizontal direction(parallel to the base).

A plane cuts the solid shape in the vertical direction(perpendicular to the base).

Question 6.

Can a plane slice a cone so that the cross-section of the cone is a triangle? Explain.

Answer:

Yes, slice of cone is triangle.

Explanation:

Vertical cross-section:

A plane cuts the solid shape in the vertical direction(perpendicular to the base).