# Lesson 11

Prisms Practice

### Problem 1

This prism has a right triangle for a base. What is the volume of the prism?

### Solution

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### Problem 2

An oblique cylinder with a base of radius 2 units is shown. The top of the cylinder can be obtained by translating the base by the directed line segment $$AB$$ which has length $$6\sqrt{2}$$ units. The segment $$AB$$ forms a $$45^\circ$$ angle with the plane of the base. What is the volume of the cylinder?

### Solution

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### Problem 3

A prism has a height of 5 inches and a volume of 80 cubic inches. Select all figures that could be the base for this prism.

A:

a square with side length 4 inches

B:

a 2 inch by 8 inch rectangle

C:

a circle with radius 2 inches

D:

a right triangle with legs 4 inches long

E:

a heart-shaped base with an area of 16 square inches

### Solution

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### Problem 4

This water bottle has a base with area $$B$$ square inches and a height of $$h$$ inches. Tyler thinks the volume of the water bottle is $$Bh$$. Elena thinks the volume is less than $$Bh$$.

Do you agree with either of them? Explain your reasoning.

### Solution

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(From Unit 5, Lesson 10.)

### Problem 5

This solid has curved sides. All cross sections parallel to the base are squares measuring 3 units on each side. The height from the base to the top is 10 units. What is the volume of this solid?

A:

30 cubic units

B:

60 cubic units

C:

90 cubic units

D:

There is not enough information to determine the volume.

### Solution

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(From Unit 5, Lesson 10.)

### Problem 6

Each small square represents 1 square centimeter.

1. Sketch and label the solid formed by rotating this two-dimensional figure around the horizontal axis shown.
2. What is the volume of this solid?

### Solution

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(From Unit 5, Lesson 9.)

### Problem 7

A solid has volume 6 cubic units and surface area 22 square units. The solid is dilated, and the image has surface area 198 square units. What is the volume of the image?

### Solution

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(From Unit 5, Lesson 8.)

### Problem 8

The Pyramid of Khufu in Giza, Egypt was the world’s tallest free-standing structure for more than 3,500 years. Its original height was about 144 meters. Its base is approximately a square with a side length of 231 meters.

The diagram shows a cross section created by dilating the base using the top of the pyramid as a center. The cross section has side length of 154 meters.

1. What scale factor was used to create the cross section?
2. What is the height of the cross section?

### Solution

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(From Unit 5, Lesson 3.)

### Problem 9

Select all statements that must be true.

A:

The angle bisector of an isosceles triangle is also the perpendicular bisector.

B:

The angle bisector of any angle divides the angle into 2 congruent parts.

C:

The median of a triangle is also the perpendicular bisector.

D:

The median of an isosceles triangles is also the angle bisector.

E:

The median of a triangle is also the angle bisector.

### Solution

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(From Unit 2, Lesson 14.)