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Question 1

A)Which statement best describes an informal argument for the formula for the volume of a cylinder?(1 point)
Responses

A cylinder is a curved lateral surface with height h and two circular bases, each with area πr2
, so its volume formula is V=2πr2h
.
A cylinder is a curved lateral surface with height h and two circular bases, each with area pi r squared , so its volume formula is upper V equals 2 pi r squared h .

A cylinder is a stack of r circles, each with an area of πr2
and a thickness of one unit, so its volume formula is V=πr3
.
A cylinder is a stack of r circles, each with an area of pi r squared and a thickness of one unit, so its volume formula is upper V equals pi r cubed .

A cylinder is a curved lateral surface with area 2πrh
and two circular bases each with area πr2
, so its volume formula is V=2πrh+2πr2
.
A cylinder is a curved lateral surface with area 2 pi r h and two circular bases each with area pi r squared , so its volume formula is upper V equals 2 pi r h plus 2 pi r squared .

A cylinder is a stack of h circles, each with an area of πr2
and a thickness of one unit, so its volume formula is V=πr2h
.
A cylinder is a stack of h circles, each with an area of pi r squared and a thickness of one unit, so its volume formula is upper V equals pi r squared h .
Question 2
A)Shelly knows the area of the base of a cylinder. What other information does she need to find its volume?(1 point)
Responses

the circumference of the base of the cylinder
the circumference of the base of the cylinder

the height of the cylinder
the height of the cylinder

the radius of the base of the cylinder
the radius of the base of the cylinder

the diameter of the base of the cylinder
the diameter of the base of the cylinder
Question 3
A)What other formula does the formula for the volume of a cylinder rely on?(1 point)
Responses

the formula for the circumference of a circle
the formula for the circumference of a circle

the formula for the surface area of a cone
the formula for the surface area of a cone

the formula for the surface area of a cylinder
the formula for the surface area of a cylinder

the formula for the area of a circle
the formula for the area of a circle
Question 4
A)Calculate the volume of a cylinder with a height of 25 millimeters and a diameter of 40 millimeters.(1 point)
Responses

1,000π mm3
1,000 pi mm cubed

10,000π mm3
10,000 pi mm cubed

40,000π mm3
40,000 pi mm cubed

4,000π mm3
4,000 pi mm cubed
Question 5
A)Calculate the volume of a cylinder with a height of 20 centimeters and a radius of 5 centimeters. Leave your answer in terms of π
.(1 point)
Responses

500π cm3
500 pi cm cubed

2,000π cm3
2,000 pi cm cubed

100π cm3

1 answer

Here are the answers to your questions:

Question 1: The best informal argument for the formula for the volume of a cylinder is:

  • A cylinder is a stack of h circles, each with an area of πr² and a thickness of one unit, so its volume formula is V = πr²h.

Question 2: If Shelly knows the area of the base of a cylinder, the other information she needs to find its volume is:

  • the height of the cylinder.

Question 3: The formula for the volume of a cylinder relies on the formula for:

  • the area of a circle.

Question 4: To calculate the volume of a cylinder with a height of 25 millimeters and a diameter of 40 millimeters:

  1. Radius = diameter / 2 = 40 mm / 2 = 20 mm.
  2. Volume V = πr²h = π(20 mm)²(25 mm) = π(400 mm²)(25 mm) = 10,000π mm³. So the answer is:
  • 10,000π mm³.

Question 5: To calculate the volume of a cylinder with a height of 20 centimeters and a radius of 5 centimeters:

  1. Volume V = πr²h = π(5 cm)²(20 cm) = π(25 cm²)(20 cm) = 500π cm³. So the answer is:
  • 500π cm³.

Let me know if you need any further assistance!