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

$$SA = 2(3 \times 4 + 3 \times 5 + 4 \times 5) = 2(12 + 15 + 20) = 2(47) = 94$$

Q: What is the volume of a cylinder with radius $$r = 2$$ and height $$h = 7$$?

$$V = \pi r^2$ h = \pi \times 4 \times 7 = 28\pi$$

Q: What is the area of a sector of a circle with radius $$r = 6$$ and central angle $$\theta = 90^\circ$$?

$$A = \frac{90}{360} \times \pi \times 6^2$ = \frac{1}{4} \times \pi \times 36 = 9\pi$$

Q: What is the lateral area of a cylinder with radius $$r = 3$$ and height $$h = 8$$?

$$LA = 2\pi r h = 2\pi \times 3 \times 8 = 48\pi$$

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

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

Q: What is the area of an equilateral triangle with side length $$s = 6$$?

$$A = \frac{\sqrt{3}}{4} s^2$ = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3}$$

Question 1

Which of the following statements about square roots is correct?

Accepted Answer

The square root of a positive number $$x is $$defined as $$\sqrt{x}.$$

Question 2

Given the equation $$(x-2)^2$$ + $$(y+3)^2 = 25$, what is the radius of the circle?

Accepted Answer

$$r = 5$$

Question 3

What is the area of a circle with radius $$r = 4$$?

Accepted Answer

$$A = 16\pi$$

Question 4

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

$$A = 25\pi - 9\pi = 16\pi$$

Question 5

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

Accepted Answer

$$c = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 6

Which formula correctly represents the surface area of a sphere with radius $$r$$?

Accepted Answer

$$SA = 4\pi r^2$

Question 7

If the circumference of a circle is $$C = 18\pi$$, what is the radius?

Accepted Answer

$$r = 9$$

Question 8

What is the area of a rectangle with length $$l = 7$$ and width $$w = 4$$?

Accepted Answer

$$A = 28$$

Question 9

Which of the following is true about congruent shapes?

Accepted Answer

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

Question 10

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

Accepted Answer

$$SA = 2(3 	imes 4 + 3 	imes 5 + 4 	imes 5) = 2(12 + 15 + 20) = 2(47) = 94$$

Question 11

What is the volume of a cylinder with radius $$r = 2$$ and height $$h = 7$$?

Accepted Answer

$$V = \pi r^2$ h = \pi 	imes 4 	imes 7 = 28\pi$$

Question 12

What is the area of a sector of a circle with radius $$r = 6$$ and central angle $$	heta = 90^\circ$$?

Accepted Answer

$$A = \frac{90}{360} 	imes \pi 	imes 6^2$ = \frac{1}{4} 	imes \pi 	imes 36 = 9\pi$$

Question 13

Which formula gives the perimeter of a square with side length $$s$$?

Accepted Answer

$$P = 4s$$

Question 14

A triangle has sides of length $$5$$, $$5$$, and $$5. $$What is the perimeter?

Accepted Answer

$$P = 15$$

Question 15

What is the lateral area of a cylinder with radius $$r = 3$$ and height $$h = 8$$?

Accepted Answer

$$LA = 2\pi r h = 2\pi 	imes 3 	imes 8 = 48\pi$$

Question 16

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 17

Which of the following is NOT a property of similar shapes?

Accepted Answer

Same size

Question 18

What is the area of an equilateral triangle with side length $$s = 6$$?

Accepted Answer

$$A = \frac{\sqrt{3}}{4} s^2$ = \frac{\sqrt{3}}{4} 	imes 36 = 9\sqrt{3}$$

Question 19

A right triangle has legs $$a = 9$$ and $$b = 12. $$What is the length of the hypotenuse?

Accepted Answer

$$c = \sqrt{9^2$ + 12^2$} = \sqrt{81 + 144} = \sqrt{225} = 15$$

Geometry Essentials for Beginning-Intermediate Algebra

Guida di studio - Domande di pratica

Study guide - Flashcard