Math Math Geometry and Measurement 5

Question 1

On a coordinate plane, what is the distance between points (1, 2) and (4, 6)?

Accepted Answer

5 units

Answer

Distance = √((4−1)² + (6−2)²) = √(9 + 16) = √25 = 5 units.

Question 2

A cone has a radius of 6 cm and a height of 8 cm. What is its volume? (Use π ≈ 3.14)

Accepted Answer

301.44 cm³

Answer

V = (1/3)πr²h = (1/3)(3.14)(36)(8) = 301.44 cm³.

Question 3

A trapezoid has parallel bases of 6 in and 10 in and a height of 4 in. What is its area?

Accepted Answer

32 in²

Answer

Area = ½ × (b₁ + b₂) × h = ½ × (6 + 10) × 4 = 32 in².

Question 4

Two parallel lines are cut by a transversal. If one interior angle is 65°, what is the measure of the co-interior (same-side interior) angle?

Accepted Answer

115°

Answer

Co-interior angles (also called consecutive interior angles) are supplementary, so 180° − 65° = 115°.

Question 5

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

Accepted Answer

50.24 in²

Answer

Area of sector = (θ/360) × πr² = (90/360) × 3.14 × 64 = 0.25 × 200.96 = 50.24 in².

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