Lesson 2

Question 1

Define volume.

Answer 1

The amount of space occupied by a three-dimensional shape.

Question 2

What is the formula for the volume of a sphere?

Answer 2

V = 4/3 π r³, where r is the radius.

Question 3

True or false: The volume of a cylinder depends on its height.

Answer 3

TRUE

Volume is calculated as V = π r² h.

Question 4

Fill in the blank: The volume of a cone is _______.

Answer 4

V = 1/3 π r² h.

Question 5

What shape has the formula V = 4/3 π r³?

Answer 5

Sphere.

Question 6

Define cylinder.

Answer 6

A three-dimensional shape with two parallel circular bases connected by a curved surface.

Question 7

What is the volume of a cylinder formula?

Answer 7

V = π r² h, where r is the radius and h is the height.

Question 8

True or false: A cone’s volume is one-third that of a cylinder with the same base and height.

Answer 8

TRUE

This is a fundamental relationship in geometry.

Question 9

Fill in the blank: The height of a cone is the perpendicular distance from the base to the _______.

Answer 9

apex.

Question 10

What is the volume of a cone with radius 3 and height 4?

Answer 10

V = 12π cubic units.

Question 11

Define radius.

Answer 11

The distance from the center of a circle or sphere to its surface.

Question 12

What is the volume of a sphere with a radius of 5?

Answer 12

V = 500/3 π cubic units.

Question 13

True or false: The volume of a shape can be negative.

Answer 13

FALSE

Volume is always a non-negative quantity.

Question 14

Fill in the blank: The base area of a cylinder is calculated as _______.

Answer 14

π r².

Question 15

What is the height of a cylinder?

Answer 15

The perpendicular distance between its two bases.

Question 16

Define cone.

Answer 16

A three-dimensional shape with a circular base tapering to a point called the apex.

Question 17

What is the relationship between a cone and a cylinder?

Answer 17

A cone’s volume is one-third that of a cylinder with the same base and height.

Question 18

Fill in the blank: The slant height of a cone is the distance from the base to the _______.

Answer 18

apex along the side.

Question 19

What is the formula for the volume of a cylinder?

Answer 19

V = π r² h.

Question 20

True or false: The volume of a sphere increases with the cube of the radius.

Answer 20

TRUE

This reflects how volume scales with size.

Question 21

Fill in the blank: The volume of a cylinder is directly proportional to its _______.

Answer 21

height.

Question 22

What is the volume of a cylinder with radius 2 and height 5?

Answer 22

V = 20π cubic units.

Question 23

Define base area.

Answer 23

The area of the bottom face of a three-dimensional shape.

Question 24

What is the volume of a cone with radius 3 and height 6?

Answer 24

V = 18π cubic units.

Question 25

True or false: The volume of a sphere is independent of its radius.

Answer 25

FALSE ## Footnote Volume depends directly on the radius.

Question 26

Fill in the blank: The **total volume** of a composite shape is the _______ of the volumes of its parts.

Answer 26

sum.

Question 27

What is the **volume** of a sphere with a radius of 1?

Answer 27

V = 4/3 π cubic units.