Let's solve each question step by step.
Question 1
A) The informal argument for the formula for the volume of a cylinder is based on thinking of a cylinder as which of the following?
Option #1: stacked squares
Option #2: stacked rectangles
Option #3: stacked circles
Option #4: stacked triangles
The best choice is Option #3: stacked circles.
Question 2
A) Which option best describes how to find the volume of a cylinder?
Option #1: Add the area of the cylinder’s base to its height.
Option #2: Multiply the area of the cylinder’s base by its height.
Option #3: Add the area of the cylinder’s lateral face to its height.
Option #4: Multiply the area of the cylinder’s lateral face by its height.
The best choice is Option #2: Multiply the area of the cylinder’s base by its height.
Question 3
A) Which two quantities could be used to find the volume of a cylinder?
Option #1: radius and diameter
Option #2: circumference and radius
Option #3: diameter and circumference
Option #4: radius and height
The best choice is Option #4: radius and height.
Question 4
A) A cylindrical grain bin on a farm has a volume of 31,400 cubic feet. Find the height of the grain bin if the cylinder’s diameter is 40 feet long. Use 3.14 for π.
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Calculate the radius:
Diameter = 40 feet
Radius = 40 / 2 = 20 feet -
Use the volume formula:
\[ V = \pi r^2 h \]
\[ 31,400 = 3.14 \times (20^2) \times h \]
\[ 31,400 = 3.14 \times 400 \times h \]
\[ 31,400 = 1256h \] -
Solve for height \(h\):
\[ h = \frac{31,400}{1256} \approx 25 \text{ ft} \]
So, \( h \approx 25 \) ft.
Question 5
A) A cylindrical recycling container has a height of 76 centimeters, but the radius is unknown. Find the radius if the container has a volume of 600,000 cm³. Round your answer to the nearest whole number.
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Use the volume formula:
\[ V = \pi r^2 h \]
\( 600,000 = 3.14 \times r^2 \times 76 \) -
Rearrange to solve for \( r^2 \):
\[ r^2 = \frac{600,000}{3.14 \times 76} \]
\[ r^2 = \frac{600,000}{238.64} \approx 2513.93 \] -
Calculate the radius \( r \):
\[ r \approx \sqrt{2513.93} \approx 50.13 \text{ cm} \]
Rounding to the nearest whole number, the radius is approximately \( 50 \) cm.
Final Answers:
- Question 1: #3
- Question 2: #2
- Question 3: #4
- Question 4: h = 25 ft
- Question 5: The radius is about 50 cm.