Lesson 1

Solids of Rotation

  • Let’s rotate two-dimensional shapes to make three-dimensional shapes.

Problem 1

Sketch the solid of rotation formed by rotating the given two-dimensional figure using the horizontal line shown as an axis of rotation.

A squiggly line above a horizontal straight line.

Problem 2

Draw a two-dimensional figure that could be rotated using a vertical axis of rotation to give the barrel shown.

An image of a brown barrel.

Problem 3

Match the two-dimensional figure and axis of rotation with the solid of rotation that can be formed by rotating the figure using that axis.

A:
A vertical dashed line with part of a triangle on the right side of line.
B:
A vertical dashed line with a part of a rectangle on the right side of the line.
C:
Vertical dashed line with a part of a circle on the right side of the line.
1:

a cylinder

2:

a sphere

3:

a cone

Problem 4

Find the area of the shaded region.

Shaded region = half of a circle with radius = 3 units, plus a rectangle with side lengths= 3 and 6 units.
(From Unit 4, Lesson 11.)

Problem 5

Technology required. Find the area of the figure.

Quadrilateral ABCE. Angles B and C = 90 degrees. Angle E = 70 degrees. Side AB = 8, side BC=10.
(From Unit 4, Lesson 11.)

Problem 6

Technology required. This stop sign is a regular octagon. It has side lengths of 12 inches. What is the area? What is the perimeter?

A stop sign.

(From Unit 4, Lesson 10.)

Problem 7

Right triangle \(ABC\) is shown. 

Select all expressions which are equal to the length of side \(BC\).

Triangle A B C. Angle C is a right angle, angle B is 55 degrees, A C is 4 point 9 units, and A B is 6 units.
A:

\(\sqrt{4.9^2+6^2}\)

B:

\(\sqrt{6^2-4.9^2}\)

C:

\(4.9\sin(55)\)

D:

\(\frac{4.9}{\sin(55)}\)

E:

\(4.9\tan(55)\)

F:

\(\frac{4.9}{\tan(55)}\)

G:

\(6\cos(55)\)

H:

\(\frac{6}{\cos(55)}\)

(From Unit 4, Lesson 6.)