Bluebook SAT Test Area and Volume 6

Question 1

A cylindrical can has diameter 10 cm and height 15 cm. What is the volume? (Leave in terms of π)

Accepted Answer

375π cm³

Answer

Radius = 5; V = π(5²)(15) = 375π cm³.

Question 2

A trapezoid has area 90 cm², height 9 cm, and one parallel side 8 cm. What is the other parallel side?

Accepted Answer

12 cm

Answer

90 = ½(8 + b₂)(9) → 20 = 8 + b₂ → b₂ = 12 cm.

Question 3

A composite figure is a 10 m × 10 m square with a triangle of base 10 m and height 6 m on top. What is the total area?

Accepted Answer

130 m²

Answer

Square = 100 m²; triangle = ½ × 10 × 6 = 30 m²; total = 130 m².

Question 4

A hemisphere (half-sphere) has radius 6 cm. What is its volume in terms of π?

Accepted Answer

144π cm³

Answer

Full sphere = (4/3)π(6³) = (4/3)π(216) = 288π; hemisphere = 144π cm³.

Question 5

If the radius of a circle is increased by 50%, by what percent does the area increase?

Accepted Answer

125%

Answer

New area = π(1.5r)² = 2.25πr²; percent increase = (2.25 − 1) × 100% = 125%.

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