OAR OAR Math Skills: Geometry 5

Question 1

A sphere has a radius of 3 in. What is its volume? (Use π ≈ 3.14)

Accepted Answer

113.04 in³

Answer

V = (4/3) × π × r³ = (4/3) × 3.14 × 27 = 113.04 in³.

Question 2

Two similar triangles have corresponding sides in a ratio of 3:5. If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?

Accepted Answer

75 cm²

Answer

The area ratio equals the square of the side ratio: (3/5)² = 9/25; larger area = 27 × (25/9) = 75 cm².

Question 3

A sector of a circle has a central angle of 90° and radius 8 cm. What is the area of the sector? (Use π ≈ 3.14)

Accepted Answer

50.24 cm²

Answer

Area = (θ/360°) × πr² = (90/360) × 3.14 × 64 = 0.25 × 200.96 = 50.24 cm².

Question 4

A line passes through points (0, 4) and (3, 10). What is the equation of the line?

Accepted Answer

y = 2x + 4

Answer

Slope = (10 − 4)/(3 − 0) = 6/3 = 2; y-intercept = 4; equation: y = 2x + 4.

Question 5

Which transformation maps a figure onto itself only if the figure has rotational symmetry?

Accepted Answer

Rotation

Answer

A rotation maps a figure onto itself only when the figure has rotational symmetry about the center of rotation.

OAR Test Practice Test

OAR Test Practice Test

OAR OAR Math Skills: Geometry 5