Volume of Cones

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base and h is the height.

Front

What does π (pi) represent in the context of a cone's volume?

Back

π (pi) is a mathematical constant approximately equal to 3.14, used to calculate the circumference and area of circles, and is essential in the volume formula for cones.

Front

If a cone has a radius of 3 cm and a height of 5 cm, what is its volume?

Back

Using the formula V = (1/3)πr²h, the volume is V = (1/3) × 3.14 × (3)² × 5 = 47.1 cm³.

Front

How does changing the height of a cone affect its volume?

Back

Increasing the height of a cone increases its volume, while decreasing the height reduces the volume, assuming the radius remains constant.

Front

What happens to the volume of a cone if the radius is doubled?

Back

If the radius is doubled, the volume increases by a factor of 4, since volume is proportional to the square of the radius (V ∝ r²).

Front

What is the relationship between the volume of a cone and a cylinder with the same base and height?

Back

The volume of a cone is one-third the volume of a cylinder with the same base and height (V_cone = (1/3)V_cylinder).

Front

How do you round the volume of a cone to the nearest tenth?

Back

To round to the nearest tenth, look at the hundredths place. If it's 5 or more, round up; if it's less than 5, round down.

Front

What is the volume of a cone with a radius of 4 inches and a height of 9 inches?

Back

Using the formula V = (1/3)πr²h, the volume is V = (1/3) × 3.14 × (4)² × 9 = 113.04 in³.

Front

What units are used for measuring the volume of a cone?

Back

Volume is typically measured in cubic units, such as cubic centimeters (cm³), cubic inches (in³), or cubic meters (m³).

Front

If a cone has a volume of 150 cm³ and a height of 10 cm, what is the radius?

Back

Using the formula V = (1/3)πr²h, rearranging gives r = sqrt((3V)/(πh)). For V = 150 cm³ and h = 10 cm, r ≈ 3.9 cm.