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
Answer:
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.
