10.5—Volume of Prisms, Cylinders, Pyramids, Cones, and Spheres

10.5 Day 1 Warm UpFind the area of each figure. Give exact answers

2. a regular hexagon with

edge length 14 m

1. an equilateral triangle with edge length 20 cm

𝐴 = 100 3 cm2𝐴 = 294 3 m2

𝐴 = 297 ft2 𝐴 = 150 + 25 3 cm2

Find the surface area of each figure. Give exact answers.

4. a regular triangular pyramid with

base edge length 10 cm and slant

height 10 cm

3. a regular square pyramid with

base edge length 9 ft and slant

height 12 ft

10.5—Volume of Prisms, Cylinders, Pyramids, Cones, and Spheres

Objective: ________ ____ volume of prisms, cylinders, pyramids, cones, and

spheres.

The volume of a solid is the number of ______ _____ contained in

its_________.

Volume is measured in cubic units.

cubic units interior

Calculate the

VOLUME OF A PRISM:

V = ____ (B = area of a base, h = height of the prism)

VOLUME OF A CYLINDER:

V = ____ (B = area of a base, h = height of the prism)

V = _______ (r = radius of a base)

Volume of a Cube with side length s: V = ______

Volume of a Rectangular Prism (a box) with length l, width w, and height h:

V = __∙__∙__

Bh

πr2h

Bh

s3

l∙w∙h

Find the volume of the right prism or the right cylinder.

1. 2. 3.

The volume of a pyramid is _____ ______the volume of the __________

with the ______ base and height.

The volume of a cone is _____ _______ the volume of the ___________

with the ______ base and height.

VOLUME OF A PYRAMID:

V = __ _____ (B = area of the base, h = height of the pyramid)

VOLUME OF A CONE:

V = __ _____ (B = area of the base, h = height of the cone)

V = __ ______ (r = radius of the base, h = height of the cone)

⅓Bh

⅓Bh

⅓ πr2h

one third

prism

samecylinder

one third

same

Find the volume of the pyramid or cone.

4. 5.

6. 7.

Find the surface area and volume of each figure. Give exact answers.

1. a cube with edge length 10 cm

2. a right cylinder with height 15 in. and base radius 8 in.

SA = 600 cm2 ; V = 1000 cm3

SA = 368𝜋 in2; V = 960𝜋 in3

10.5—Volume of Prisms, Cylinders, Pyramids, Cones, and Spheres

10.5 Day 2 Warm Up

VOLUME OF A SPHERE:

V = __ ____ (r = radius of the sphere)4/3 πr3

Find the volume of the sphere.

6. 7. 8.

All spheres are similar to each other. Use problems 6 and 7 above to answer the following.

What is the ratio of their radii?

Based on what you learned in 10.4, what is the ratio of their surface areas?

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6. 7.

What is the ratio of their volumes?

Given two spheres have radii with a ratio of 𝑎

𝑏, what is the ratio of their volumes?

18 in

9. The two cylinders are similar.

a. Find the similarity ratio for the two cylinders.

b. Find the ratio of their surface areas.

c. Find the ratio of their volumes.

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