SAT Geometry & Trigonometry

Question 1

A circle has a radius of 5. What is the area of the circle?

Accepted Answer

25π

Answer

Area of a circle = πr², so π(5²) = 25π.

Question 2

In a right triangle, one leg is 3 and the hypotenuse is 5. What is the length of the other leg?

Accepted Answer

4

Answer

By the Pythagorean theorem: 3² + b² = 5² → b² = 25 − 9 = 16 → b = 4.

Question 3

What is the measure of each interior angle of a regular hexagon?

Accepted Answer

120°

Answer

Sum of interior angles = (6−2)×180° = 720°; each angle = 720°÷6 = 120°.

Question 4

If sin(θ) = 3/5 for an acute angle θ, what is cos(θ)?

Accepted Answer

4/5

Answer

Using sin²θ + cos²θ = 1: cos²θ = 1 − 9/25 = 16/25, so cos θ = 4/5.

Question 5

What is the volume of a cylinder with radius 3 and height 4?

Accepted Answer

36π

Answer

Volume = πr²h = π(3²)(4) = 36π.

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