OAR OAR Math Skills: Geometry 4

Question 1

The volume of a cube is 125 in³. What is the length of one edge?

Accepted Answer

5 in

Answer

V = s³ → s = ∛125 = 5 in.

Question 2

A right triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg?

Accepted Answer

12

Answer

b² = 13² − 5² = 169 − 25 = 144; b = 12 (the 5-12-13 Pythagorean triple).

Question 3

An exterior angle of a triangle measures 110°. If one non-adjacent interior angle is 45°, what is the other non-adjacent interior angle?

Accepted Answer

65°

Answer

An exterior angle equals the sum of the two non-adjacent interior angles: 110° − 45° = 65°.

Question 4

What is the midpoint of the segment connecting (−4, 2) and (6, −8)?

Accepted Answer

(1, −3)

Answer

Midpoint = ((−4+6)/2, (2+(−8))/2) = (2/2, −6/2) = (1, −3).

Question 5

A cone has a radius of 6 cm and a height of 9 cm. What is its volume? (Use π ≈ 3.14)

Accepted Answer

339.12 cm³

Answer

V = (1/3) × π × r² × h = (1/3) × 3.14 × 36 × 9 = 339.12 cm³.

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