What is the volume of a cylinder with a radius of 5 and a height of 3? What is the volume of a cylinder with a diameter of 10 and a height of 25? Which of the following is NOT equa... What is the volume of a cylinder with a radius of 5 and a height of 3? What is the volume of a cylinder with a diameter of 10 and a height of 25? Which of the following is NOT equal to the others? How many quarts are equivalent to 8 gallons? What is the volume of a cylinder with a diameter of 6 and a height of 10? A cylinder has a base area of 25π unit². If its volume is 250π unit³, what is its height? Which of the following units is NOT used to measure volume? The volume of a cylinder is 250π cm³, and its height is 10 cm. What is its radius? Which of the two containers can hold more water? If the height of the pyramid to your right is 14, what is its volume? Read more

Steps to Solve

1. Calculate the volume of the first cylinder (Question 11)

The formula for the volume of a cylinder is given by

$$ V = \pi r^2 h $$

where ( r ) is the radius and ( h ) is the height. For a cylinder with a radius of 5 and height of 3, we substitute:

• ( r = 5 )
• ( h = 3 )

Calculating:

$$ V = \pi (5)^2 (3) = \pi (25)(3) = 75\pi $$

So, the answer is ( \text{D. } 75\pi ).

2. Calculate the volume of the second cylinder (Question 12)

For the second question, we have a diameter of 10, so the radius ( r ) is

$$ r = \frac{10}{2} = 5 $$

Now, the height ( h = 25 ). Using the same volume formula:

$$ V = \pi r^2 h = \pi (5)^2 (25) = \pi (25)(25) = 625\pi $$

The answer is ( \text{B. } 625\pi ).

3. Analyze unit measurements (Question 13)

The options are different units of weight and volume. To find which is NOT equal to the others, convert everything to ounces:

• 1 lb = 16 oz
• ( \frac{1}{4} ) gallon = 32 oz

The answer is ( \text{C. } 16 \text{ oz} ) since it is not equal to the other measurements.

4. Convert gallons to quarts (Question 14)

Knowing 1 gallon = 4 quarts, for 8 gallons we have:

$$ 8 \text{ gallons} \times 4 \text{ quarts/gallon} = 32 \text{ quarts} $$

The answer is ( \text{D. } 32 ).

5. Volume of the cylinder with diameter 6 (Question 15)

For this question, ( r = \frac{6}{2} = 3 ) and ( h = 10 ):

$$ V = \pi r^2 h = \pi (3)^2 (10) = \pi (9)(10) = 90\pi $$

The answer is ( \text{D. } 90\pi ).

6. Find the height of the cylinder (Question 16)

Given the volume is ( 250\pi ) and the base area is ( 25\pi ), we use ( V = A \cdot h ):

$$ 250\pi = 25\pi \cdot h $$

Dividing both sides by ( 25\pi ):

$$ h = \frac{250\pi}{25\pi} = 10 $$

The answer is ( \text{B. } 10 \text{ units} ).

7. Calculate the radius from volume (Question 17)

For a volume of ( 250\pi ) cm(^3) and height 10 cm, use the volume formula:

$$ 250\pi = \pi r^2 (10) $$

Dividing both sides by ( 10\pi ):

$$ r^2 = 25 \Rightarrow r = \sqrt{25} = 5 \text{ cm} $$

The answer is ( \text{A. } 5 \text{ cm} ).

8. Compare container volumes (Question 19)

To determine which container holds more water, calculate their volumes using the cylinder formula.

For container A, the radius is ( 6 ) and height is ( 26 ):

$$ V_A = \pi(6)^2(26) = \pi(36)(26) = 936\pi $$

For container B, the radius is ( 12 ) and height is ( 8 ):

$$ V_B = \pi(12)^2(8) = \pi(144)(8) = 1152\pi $$

Hence, ( \text{B holds more since } 1152\pi > 936\pi ). So, the answer is ( \text{B. } \text{ container B} ).

9. Volume of the pyramid (Question 20)

The volume of a pyramid is given by

$$ V = \frac{1}{3} \cdot \text{Base Area} \cdot h $$

The base is 15 (length) * 3 (width) = 45 square units, and height is 14:

$$ V = \frac{1}{3} \cdot 45 \cdot 14 = \frac{630}{3} = 210 $$

The answer is ( \text{C. } 210 ).