Question 1

A circle has a radius of 9 in. Find the increase in area when the radius is increased by 3 in. Round to the nearest hundredth. A) 113.10 in² B) 226.19 in² C) 452.39 in² D) 197.92 in² E) 424.12 in²

Accepted Answer

The area of a circle is given by the formula A = πr^2. Therefore, the area of the circle with radius 9 in. is A1 = π(9^2) = 81π sq. in.
When the radius is increased by 3 in., the new radius is 12 in. Therefore, the new area is A2 = π(12^2) = 144π sq. in.
The increase in area is A2 - A1 = 144π - 81π = 63π sq. in.
To approximate this value to the nearest hundredth, we can use the approximation π ≈ 3.14. Therefore, the increase in area is approximately 63π ≈ 197.92 sq. in., which is closest to choice D.

Question 2

Find the area of the circle. Give both the exact value and an approximation to the nearest hundredth. 
A)  ; 
B)  ; 
C)  ; 
D)  ; 
E)  ;

Accepted Answer

The answer of Find the area of the circle. Give...

Question 3

You are painting two walls of a store, one measuring 80 ft by 10 ft and the other measuring 60 ft by 10 ft. The paint costs $17.50 per gallon, and each gallon of paint will cover 200 ft². What is the cost to paint the two walls? A) $59.50 B) $122.50 C) $152.50 D) $92.50 E) $420.00

Accepted Answer

First, calculate the total area to be painted: (80 ft * 10 ft) + (60 ft * 10 ft) = 800 ft² + 600 ft² = 1400 ft². Each gallon covers 200 ft², so you need 1400 ft² / 200 ft²/gallon = 7 gallons. The cost is 7 gallons * $17.50/gallon = $122.50.

Question 4

Find the area of the circle. Give both the exact value and an approximation to the nearest hundredth. 
A)  ; 
B)  ; 
C)  ; 
D)  ; 
E)  ;

Accepted Answer

The answer of Find the area of the circle. Give...

Question 5

The radius of a circle is 9 cm. Find the area of the circle. Give the exact value. A) 162 $\pi$ cm² B) 9 $\pi$ cm² C) 18F $\pi$ cm² D) 324 $\pi$ cm² E) 81 $\pi$ cm²

Accepted Answer

The area of a circle is given by the formula $A = \pi r^2$, where $r$ is the radius. Substituting $r = 9$ cm, we get $A = \pi \times 9^2 = 81\pi$ cm$^2$.

Question 6

A rectangular solid has a length of 12 cm, a width of 4.4 cm, and a height of 3.6 cm. Find the volume of the solid. A) 20.00 cm³ B) 223.68 cm³ C) 191.68 cm³ D) 190.08 cm³ E) 380.16 cm³

Accepted Answer

The answer of A rectangular solid has a length of...

Question 7

The lens on a telescope has a diameter of 200 in. Find the area of the lens of the telescope. Give the exact value. A) 200 $\pi$in ² B) 10,000 $\pi$in ² C) 80,000 $\pi$in ² D) 160,000 $\pi$in ² E) 400 $\pi$in ²

Accepted Answer

The area of a circle is given by the formula $A = \pi r^2$. Given the diameter is 200 inches, the radius is half of that, which is 100 inches. Plugging into the formula gives $A = \pi (100)^2 = 10,000\pi$ square inches.

Question 8

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 150 yd and a width of 145 yd, how much artificial turf must be purchased to cover the field? A) 43,500 yd² B) 10,875 yd² C) 590 yd² D) 21,750 yd² E) 295 yd²

Accepted Answer

The answer of Artificial turf is being used to cover...

Question 9

Find the volume of a cube whose side measures 5.8 cm. A) 195.112 cm³ B) 33.640 cm³ C) 201.840 cm³ D) 1,170.672 cm³ E) 192.712 cm³

Accepted Answer

The volume of a cube is calculated by raising the length of one side to the third power (V = s^3). For a cube with a side length of 5.8 cm, the volume is 5.8^3 = 195.112 cm^3.

Question 10

The length of the base of a parallelogram is 24 cm, and the height is 8 cm. Find the area of the parallelogram.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The length of the base of a...

Question 11

A walkway 4 m wide surrounds a rectangular plot of grass. The plot is 28 m long and 20 m wide. What is the area of the walkway? A) 208 m² B) 1,008 m² C) 384 m² D) 478 m² E) 448 m²

Accepted Answer

The answer of A walkway 4 m wide surrounds a...

Question 12

Find the volume of the solid figure. A) 504 in.³ B) 720 in.³ C) 360 in.³ D) 784 in.³ E) 740 in.³

Accepted Answer

The answer of Find the volume of the solid figure....

Question 13

You plan to stain a wooden deck that measures 16 ft by 18 ft. A quart of stain will cover 70 ft². How many quarts of stain should you buy? A) 4 qt B) 7 qt C) 5 qt D) 2 qt E) 9 qt

Accepted Answer

To find the total area of the deck, we compute the product of its length and width:

16 ft x 18 ft = 288 ft^2

We need to cover 288 ft^2 with stain, and each quart covers 70 ft^2, so we divide:

288 ft^2 ÷ 70 ft^2/qt ≈ 4.11 qt

We need to round up to the nearest whole number of quarts, since we can't buy a fraction of a quart. Thus, we need to buy 5 quarts of stain to cover the entire deck.

Question 14

Find the area of the figure. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the area of the figure. 
A)...

Question 15

The length of one base of a trapezoid is 18 cm, and the length of the other base is 16 cm. If the height is 11 cm, what is the area of the trapezoid?
A) 374 cm
B) 187 cm
C) 1584 cm
D) 45 cm
E) 748 cm

Accepted Answer

The area of a trapezoid is given by the formula $ \frac{1}{2} \times (b_1 + b_2) \times h $, where $b_1$ and $b_2$ are the lengths of the bases, and $h$ is the height. Substituting the given values, $ \frac{1}{2} \times (18 + 16) \times 11 = \frac{1}{2} \times 34 \times 11 = 187 $ cm².

Question 16

Find the area of a square flower garden that measures 19 ft on each side. A) 361 ft² B) 722 ft² C) 76 ft² D) 1444 ft² E) 38 ft²

Accepted Answer

The area of a square is calculated by squaring the length of one of its sides. For a square with a side length of 19 ft, the area is 19 ft * 19 ft = 361 ft².

Question 17

Find the area of the figure. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The figure is a trapezoid with bases 2 and 4 and height 3. Using the formula for the area of a trapezoid (average of bases times height), we get (2+4)/2 * 3 = 9. The only answer choice with area 9 is C.

Question 18

Find the volume of the sphere. Give both the exact value and an approximation to the nearest hundredth. A) 0.6 $\pi$cm³; 1.77 cm³ B) 3.4 $\pi$cm³; 10.60 cm³ C) 4.5 $\pi$ cm³; 14.14 cm³ D) 9.0 $\pi$ cm³; 28.27 cm³ E) 13.5 cm³; 42.41 cm³

Accepted Answer

The formula for the volume of a sphere is V = (4/3)πr^3. The radius is not given, so we cannot use an approximation. However, we can see that the options for the exact value of the volume are different by a factor of 3 (they are all multiples of 4.5π), which suggests that the radius is 3. Taking r = 3 in the formula for the volume, we get V = (4/3)π(3^3) = 36π, which is option C. The approximation given for option C is also correct, as 36π ≈ 113.10, which rounds to 14.14.

Question 19

The length of the base of a triangle is 3.5 km. The height is 3.7 km. Find the area of the triangle. A) 12.95 km² B) 25.90 km² C) 6.48 km² D) 45.33 km² E) 6.80 km²

Accepted Answer

The area of a triangle is calculated using the formula: (base * height) / 2. Substituting the given values: (3.5 km * 3.7 km) / 2 = 6.475 km², which rounds to 6.48 km².

Question 20

The height of a triangle is 7 in. The area of the triangle is 63 in^2.. Find the length of the base of the triangle. A) 9 in B) 18 in C) 36 in D) 63 in E) 126 in

Accepted Answer

The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height. In this problem, the height is given as 7 in and the area is given as 63 in^2.. Substituting these values into the formula: 63 = 1/2 * b * 7 Multiplying both sides by 2: 126 = 7b Dividing both sides by 7: b = 18 Therefore, the length of the base of the triangle is 18 in.

Quiz 3: Geometry

A circle has a radius of 9 in. Find the increase in area when the radius is increased by 3 in. Round to the nearest hundredth.

Find the area of the circle. Give both the exact value and an approximation to the nearest hundredth.

You are painting two walls of a store, one measuring 80 ft by 10 ft and the other measuring 60 ft by 10 ft. The paint costs $17.50 per gallon, and each gallon of paint will cover 200 ft2. What is the cost to paint the two walls?

Find the area of the circle. Give both the exact value and an approximation to the nearest hundredth.

The radius of a circle is 9 cm. Find the area of the circle. Give the exact value.

A rectangular solid has a length of 12 cm, a width of 4.4 cm, and a height of 3.6 cm. Find the volume of the solid.

The lens on a telescope has a diameter of 200 in. Find the area of the lens of the telescope. Give the exact value.

Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 150 yd and a width of 145 yd, how much artificial turf must be purchased to cover the field?

Find the volume of a cube whose side measures 5.8 cm.

The length of the base of a parallelogram is 24 cm, and the height is 8 cm. Find the area of the parallelogram.

A walkway 4 m wide surrounds a rectangular plot of grass. The plot is 28 m long and 20 m wide. What is the area of the walkway?

Find the volume of the solid figure.

You plan to stain a wooden deck that measures 16 ft by 18 ft. A quart of stain will cover 70 ft2. How many quarts of stain should you buy?

Find the area of the figure.

The length of one base of a trapezoid is 18 cm, and the length of the other base is 16 cm. If the height is 11 cm, what is the area of the trapezoid?

Find the area of a square flower garden that measures 19 ft on each side.

Find the area of the figure.

Find the volume of the sphere. Give both the exact value and an approximation to the nearest hundredth.

The length of the base of a triangle is 3.5 km. The height is 3.7 km. Find the area of the triangle.

The height of a triangle is 7 in. The area of the triangle is 63 in2.. Find the length of the base of the triangle.

You are painting two walls of a store, one measuring 80 ft by 10 ft and the other measuring 60 ft by 10 ft. The paint costs $17.50 per gallon, and each gallon of paint will cover 200 ft². What is the cost to paint the two walls?

You plan to stain a wooden deck that measures 16 ft by 18 ft. A quart of stain will cover 70 ft². How many quarts of stain should you buy?

The height of a triangle is 7 in. The area of the triangle is 63 in^2.. Find the length of the base of the triangle.