Unit 6 Review

Cory uses the following diagram to explain what the Pythagorean theorem means. Which is the correct explanation?

• The sum of the areas of the two smaller squares is less than the area of the largest square.

• The sum of the areas of the two smaller squares is equal to the area of the largest square.

• The sum of one side length from each of the two smaller squares is greater than one side length of the larger square.

• The sum of one side length from each of the two smaller squares is equal to one side length of the larger square.

Tina measures the distances between three cities on a map. The distances between the three cities are 45 miles, 56 miles, and 72 miles. Do the positions of the three cities form a right triangle?

• Yes

• No

A 20-foot ladder leaning against a wall is used to reach a window that is 17 feet above the ground. How far from the wall is the bottom of the ladder? Round to the nearest tenth of a foot.

• 10.4 ft.

• 10.6 ft.

• 10.5 ft.

A slide was installed at the local swimming pool, what is the length of the slide?

• 21.47 ft.

• 13.78 ft.

• 4.35 ft.

• 7.61 ft.

A right triangle has side lengths 33 inches, 56 inches, and 65 inches. What are the lengths of the legs and why?

• 33 and 56 inches, because 33 + 56 > 65

• 33 and 56 inches, because they are the two shortest sides.

• 33 and 56 inches, because the hypotenuse is one of the legs.

• 33 and 65 inches, because 33² + 56² = 65²

Find the distance between each pair of points. Round to the nearest hundredth.

(-2, 3), (4, -1)

• 6.32

• 12.65

• 2.83

• 4

Find the distance between each pair of points. Round to the nearest tenth.

(-5, 2), (5, -2)

• 6.32

• 3.7

• 5.3

• 10.8

When completely inflated, a small beach ball has a diameter of 4.6 inches. What is the volume of the beach ball?

Use 𝜋 ≈ 3.14 and round your answer to the nearest whole number.

• 50 in³

• 49 in³

• 51 in³

• 52 in³

Jerry is building a sandcastle. He has a plastic cone that is 7 inches tall with a radius of 4.6 inches that he will use for part of the sandcastle. What is the volume of the cone?

Use 𝜋 ≈ 3.14 and round your answer to the nearest whole number.

• 155 in³

• 156 in³

• 154 in³

• 153 in³

At the pet store, Vijay is deciding which fish tank to purchase for his betta fish. The store has a cylindrical fish tank that is 10 inches tall with a diameter of 10 inches. What is the volume of the cylindrical fish tank?

Use 𝜋 ≈ 3.14 and round your answer to the nearest whole number.

• 786 in³

• 784 in³

• 785 in³

• 783 in³