$$A = \frac{1}{6}\pi \times 4^2$

$$s = 2\pi r \frac{\theta}{360}$$

$$V = \pi r^2$ h = \pi \times 2^2$ \times 10 = 40\pi$$

$$SA = 4\pi r^2$ = 4\pi \times 25 = 100\pi$$

Question 1

Which of the following statements about square roots is correct?

Accepted Answer

$$\sqrt{x} is $$only defined for $$x \geq 0$$

Question 2

If two lines are perpendicular, which of the following is true about their slopes?

Accepted Answer

Their slopes are negative reciprocals

Question 3

Which property distinguishes congruent shapes from similar shapes?

Accepted Answer

Congruent shapes have the same shape, angles, proportions, and size

Question 4

What is the area of a circle with radius $$r$$?

Accepted Answer

$$A = \pi r^2$

Question 5

A small circle of radius $$3 is $$placed inside a large circle of radius $$5. $$What is the area of the region between the two circles?

Accepted Answer

$$A = \pi(5^2$ - 3^2$)$$

Question 6

What is the circumference of a circle with radius $$r$$?

Accepted Answer

$$C = 2\pi r$$

Question 7

The radius of a circle is $$4. $$What is the area of a $$60^\circ$$ sector?

Accepted Answer

$$A = \frac{1}{6}\pi 	imes 4^2$

Question 8

What is the length of an arc of a circle with radius $$r$$ and central angle $$	heta (in $$degrees)?

Accepted Answer

$$s = 2\pi r \frac{	heta}{360}$$

Question 9

If an inscribed angle in a circle intercepts an arc of $$80^\circ$$, what is the measure of the inscribed angle?

Accepted Answer

$$40^\circ$$

Question 10

Given the equation $$(x-3)^2$$ + $$(y+2)^2 = 49$, what is the center and radius of the circle?

Accepted Answer

Center $$(3, -2)$$, radius $$7$$

Question 11

What is the area and perimeter of a triangle with base $$b = 6$$ and height $$h = 4$$?

Accepted Answer

Area $$A = 12$$, Perimeter $$P = 6 + 4 + \sqrt{6^2$ + 4^2$}$$

Question 12

What is the surface area of a rectangular prism with length $$l = 3$$, width $$w = 4$$, and height $$h = 5$$?

Accepted Answer

$$SA = 2(lw + lh + wh) = 2(12 + 15 + 20) = 94$$

Question 13

What is the volume of a cylinder with radius $$r = 2$$ and height $$h = 10$$?

Accepted Answer

$$V = \pi r^2$ h = \pi 	imes 2^2$ 	imes 10 = 40\pi$$

Question 14

What is the surface area of a sphere with radius $$r = 5$$?

Accepted Answer

$$SA = 4\pi r^2$ = 4\pi 	imes 25 = 100\pi$$

Question 15

What is the length of the hypotenuse of a right triangle with sides $$a = 6$$ and $$b = 8$$?

Accepted Answer

$$c = \sqrt{6^2$ + 8^2$} = 10$$

Question 16

Which formula gives the area of a rectangle with length $$l$$ and width $$w$$?

Accepted Answer

$$A = l 	imes w$$

Question 17

A square has side length $$s = 7. $$What is its perimeter?

Accepted Answer

$$P = 4s = 28$$

Question 18

What is the volume of a sphere with radius $$r = 3$$?

Accepted Answer

$$V = \frac{4}{3}\pi r^3$ = \frac{4}{3}\pi 	imes 27 = 36\pi$$

Question 19

Which of the following best describes the difference between surface area and volume?

Accepted Answer

Surface area is measured in square units, volume in cubic units

Geometry Essentials for Precalculus: Circles, Triangles, and Solids

Study Guide - Practice Questions