SAT Geometry & Trigonometry 3

Question 1

Which equation represents a circle with center (2, −3) and radius 4?

Accepted Answer

(x−2)² + (y+3)² = 16

Answer

Standard form is (x−h)² + (y−k)² = r²; with (h,k)=(2,−3) and r=4, this gives (x−2)² + (y+3)² = 16.

Question 2

What is the surface area of a cube with side length 3?

Accepted Answer

54

Answer

A cube has 6 square faces; SA = 6s² = 6(3²) = 54.

Question 3

An inscribed angle intercepts an arc of 100°. What is the measure of the inscribed angle?

Accepted Answer

50°

Answer

The inscribed angle theorem states an inscribed angle equals half its intercepted arc: 100° ÷ 2 = 50°.

Question 4

In right triangle ABC, AB = 7, BC = 24, and angle B = 90°. What is sin(A)?

Accepted Answer

24/25

Answer

Hypotenuse AC = √(7²+24²) = √625 = 25; sin(A) = opposite/hypotenuse = BC/AC = 24/25.

Question 5

A right cone has a base radius of 3 and a height of 4. What is its volume?

Accepted Answer

12π

Answer

Volume of a cone = (1/3)πr²h = (1/3)π(9)(4) = 12π.

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