ATDH Quantitative Reasoning: Geometry and Measurement 5

Question 1

A cylindrical container of disinfectant has a radius of 3 cm and a height of 10 cm. What is its volume?

Accepted Answer

90π cm³

Answer

V = πr²h = π × 9 × 10 = 90π cm³.

Question 2

What is the distance between the points (1, 2) and (7, 10) on a coordinate plane?

Accepted Answer

10

Answer

Distance = √((7−1)² + (10−2)²) = √(36 + 64) = √100 = 10.

Question 3

A dental office orders 3 gallons of distilled water. How many quarts is this?

Accepted Answer

12 quarts

Answer

There are 4 quarts in a gallon, so 3 × 4 = 12 quarts.

Question 4

A trapezoid has parallel bases of 8 cm and 12 cm and a height of 5 cm. What is its area?

Accepted Answer

50 cm²

Answer

Area = ½(8 + 12) × 5 = 10 × 5 = 50 cm².

Question 5

Triangle A has sides 3, 4, and 5. Triangle B is similar, and its side corresponding to 3 measures 9. What is the longest side of Triangle B?

Accepted Answer

15

Answer

The scale factor is 9 ÷ 3 = 3, so the longest side is 5 × 3 = 15.

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