Answer :
Sure! Let's solve each of these questions step-by-step:
Question 11:
To find the volume of a cylinder, the formula is:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
Given a radius of 5 and a height of 3, the volume can be calculated as:
[tex]\[ \text{Volume} = \pi \times 5^2 \times 3 = \pi \times 25 \times 3 = 75\pi \][/tex]
The correct answer is D. [tex]\(75\pi\)[/tex].
Question 12:
Again, using the formula for the volume of a cylinder:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
The diameter is given as 10, so the radius is 5 (since radius is half of the diameter). The height is 25.
[tex]\[ \text{Volume} = \pi \times 5^2 \times 25 = \pi \times 25 \times 25 = 625\pi \][/tex]
The correct answer is B. [tex]\(625\pi\)[/tex].
Question 13:
We need to find which option is NOT equal to the others. Let's look at the options:
- A. [tex]\(1 \text{ lb} = 16 \text{ oz}\)[/tex]
- C. [tex]\(16 \text{ oz} = 16 \text{ oz}\)[/tex]
- B. [tex]\(\frac{1}{4} \text{ gallon}\)[/tex] is not equal to 16 oz. Since 1 gallon = 128 oz, [tex]\(\frac{1}{4}\)[/tex] gallon is 32 oz.
- D. [tex]\(\frac{1}{2000} \text{ short ton} = 16 \text{ oz}\)[/tex] (since a short ton is 2000 lbs or 32000 oz).
Option B ([tex]\(\frac{1}{4} \text{ gallon} = 32 \text{ oz}\)[/tex]) is not equal.
The correct answer is B.
Question 14:
1 gallon equals 4 quarts. So, for 8 gallons:
[tex]\[ 8 \times 4 = 32 \text{ quarts} \][/tex]
The correct answer is not listed because it should be 32.
Question 15:
Using the formula for the volume of a cylinder:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
The diameter is 6, so the radius is 3. Height is given as 10.
[tex]\[ \text{Volume} = \pi \times 3^2 \times 10 = \pi \times 9 \times 10 = 90\pi \][/tex]
The correct answer is D. [tex]\(90\pi\)[/tex].
Question 16:
Given a base area and volume, to find the height use:
[tex]\[ \text{Volume} = \text{base area} \times \text{height} \][/tex]
Solving for height:
[tex]\[ \text{height} = \frac{\text{Volume}}{\text{base area}} = \frac{250\pi}{25\pi} = 10 \][/tex]
The correct answer is B. 10 units.
Question 17:
A unit used to measure volume is one that represents a three-dimensional space. The options are:
- A. liter (volume unit)
- B. cubic meter (volume unit)
- C. quart (volume unit)
- D. square meter (area unit)
Square meter is not a volume unit.
The correct answer is D. square meter.
Question 18:
Given the volume and height of a cylinder, we need to find the radius. The formula for volume:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
Solving for the radius:
[tex]\[ 250\pi = \pi \times \text{radius}^2 \times 10 \][/tex]
Divide by [tex]\(\pi \times 10\)[/tex]:
[tex]\[ \text{radius}^2 = 25 \][/tex]
[tex]\[ \text{radius} = \sqrt{25} = 5 \][/tex]
The correct answer is A. 5 cm.
Question 19:
Without more details about containers A and B, such as their dimensions or capacities, we can't decide which holds more water.
The correct answer is D. There is not enough information given.
Question 20:
For the volume of a pyramid, the formula is:
[tex]\[ \text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Without the base area given, the volume can't be determined.
The volume can't be accurately calculated with the information provided.
Please let me know if you need further clarifications!
Question 11:
To find the volume of a cylinder, the formula is:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
Given a radius of 5 and a height of 3, the volume can be calculated as:
[tex]\[ \text{Volume} = \pi \times 5^2 \times 3 = \pi \times 25 \times 3 = 75\pi \][/tex]
The correct answer is D. [tex]\(75\pi\)[/tex].
Question 12:
Again, using the formula for the volume of a cylinder:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
The diameter is given as 10, so the radius is 5 (since radius is half of the diameter). The height is 25.
[tex]\[ \text{Volume} = \pi \times 5^2 \times 25 = \pi \times 25 \times 25 = 625\pi \][/tex]
The correct answer is B. [tex]\(625\pi\)[/tex].
Question 13:
We need to find which option is NOT equal to the others. Let's look at the options:
- A. [tex]\(1 \text{ lb} = 16 \text{ oz}\)[/tex]
- C. [tex]\(16 \text{ oz} = 16 \text{ oz}\)[/tex]
- B. [tex]\(\frac{1}{4} \text{ gallon}\)[/tex] is not equal to 16 oz. Since 1 gallon = 128 oz, [tex]\(\frac{1}{4}\)[/tex] gallon is 32 oz.
- D. [tex]\(\frac{1}{2000} \text{ short ton} = 16 \text{ oz}\)[/tex] (since a short ton is 2000 lbs or 32000 oz).
Option B ([tex]\(\frac{1}{4} \text{ gallon} = 32 \text{ oz}\)[/tex]) is not equal.
The correct answer is B.
Question 14:
1 gallon equals 4 quarts. So, for 8 gallons:
[tex]\[ 8 \times 4 = 32 \text{ quarts} \][/tex]
The correct answer is not listed because it should be 32.
Question 15:
Using the formula for the volume of a cylinder:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
The diameter is 6, so the radius is 3. Height is given as 10.
[tex]\[ \text{Volume} = \pi \times 3^2 \times 10 = \pi \times 9 \times 10 = 90\pi \][/tex]
The correct answer is D. [tex]\(90\pi\)[/tex].
Question 16:
Given a base area and volume, to find the height use:
[tex]\[ \text{Volume} = \text{base area} \times \text{height} \][/tex]
Solving for height:
[tex]\[ \text{height} = \frac{\text{Volume}}{\text{base area}} = \frac{250\pi}{25\pi} = 10 \][/tex]
The correct answer is B. 10 units.
Question 17:
A unit used to measure volume is one that represents a three-dimensional space. The options are:
- A. liter (volume unit)
- B. cubic meter (volume unit)
- C. quart (volume unit)
- D. square meter (area unit)
Square meter is not a volume unit.
The correct answer is D. square meter.
Question 18:
Given the volume and height of a cylinder, we need to find the radius. The formula for volume:
[tex]\[ \text{Volume} = \pi \times \text{radius}^2 \times \text{height} \][/tex]
Solving for the radius:
[tex]\[ 250\pi = \pi \times \text{radius}^2 \times 10 \][/tex]
Divide by [tex]\(\pi \times 10\)[/tex]:
[tex]\[ \text{radius}^2 = 25 \][/tex]
[tex]\[ \text{radius} = \sqrt{25} = 5 \][/tex]
The correct answer is A. 5 cm.
Question 19:
Without more details about containers A and B, such as their dimensions or capacities, we can't decide which holds more water.
The correct answer is D. There is not enough information given.
Question 20:
For the volume of a pyramid, the formula is:
[tex]\[ \text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Without the base area given, the volume can't be determined.
The volume can't be accurately calculated with the information provided.
Please let me know if you need further clarifications!
