A cone has a diameter of 8 units and a height of 8 units. Its radius is A. 2 B. 4 C. 8 D. 16 units, and its volume is A. 66.99 B. 133.97 C. 401.92 D. 535.89 cubic units. A cylinder with the same height and radius as the cone will have a volume of A. 66.99 B. 133.97 C. 401.92 D. 535.89 cubic units. If a sphere has the same radius as the cylinder, its volume is A. Half B. Two-thirds C. Four-thirds the volume of the cylinder.

Question

1) A cone has a diameter of 8 units and a height of 8 units. Its radius is

A. 2 B. 4 C. 8 D. 16 units,

2) and its volume is A. 66.99 B. 133.97 C. 401.92 D. 535.89 cubic units.

3) A cylinder with the same height and radius as the cone will have a volume of A. 66.99 B. 133.97 C. 401.92 D. 535.89 cubic units.

4) If a sphere has the same radius as the cylinder, its volume is A. Half B. Two-thirds C. Four-thirds the volume of the cylinder

1) B. 4 units

2) B. 133.97 cubic units

3) C. 401.92 cubic units

4) B. Two-thirds the volume of the cylinder.

Explanation:

1)In the above question, we are given the following values.

A cone has a diameter of 8 units and a height of 8 units. We are asked to find the radius.

The formula for radius = Diameter ÷ 2

The radius of the cone = 8 units ÷ 2 = 4 units.

2) We are asked to find the volume of the cone in question 1

Volume of the cone = 1/3πr²h

r = 4 units, h = 8 units, π = 3.14

= 1/3 × 3.14 × 4² × 8

= 133.97 cubic units.

3) We are asked to find the volume of a cylinder if it has same height and radius as the cone in question 1

Volume of a cylinder = πr²h

r = 4 units

h = 8 units

Volume of a cylinder = 3.14 × 4² × 8

= 401.92 cubic units.

4) If a sphere has the same radius as the cylinder, its volume is

The radius of the cylinder = 4 units

Volume of a sphere = 4/3πr³

π = 3.14

= 4/3 × π × 4³

= 268.08257311cubic units

Approximately = 268.08 cubic units.

The volume of the cylinder = 401.92 cubic units,

Two thirds of the volume of the cylinder = 2/3 × 401.92 = 268

Therefore, if a sphere has the same radius as the cylinder, its volume is 268.08 cubic units is Two-thirds the volume of the cylinder.

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