Find the Volume of the Cone Mixed Practice

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 geometry?

Back

π (pi) is a mathematical constant approximately equal to 3.14, representing the ratio of the circumference of a circle to its diameter.

Front

If a cone has a radius of 3 mm and a height of 9 mm, what is its volume?

Back

Using the formula V = (1/3)πr²h, the volume is V = (1/3) * 3.14 * (3)² * 9 = 84.78 mm³, rounded to 84.8 mm³.

Front

How do you round a number to the nearest tenth?

Back

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.

Front

What is the relationship between the diameter and radius of a cone?

Back

The radius is half of the diameter. If the diameter is 6 cm, the radius is 3 cm.

Front

What is the slant height of a cone?

Back

The slant height is the distance from the top of the cone to the edge of the base along the side of the cone.

Front

How do you calculate the volume of a cone with a diameter of 6 cm and a height of 7 cm?

Back

First, find the radius: r = diameter/2 = 3 cm. Then use the formula V = (1/3)πr²h = (1/3) * 3.14 * (3)² * 7 = 21.12 cm³.

Front

What is the volume of a cone with a radius of 5 cm and a height of 10 cm?

Back

Using the formula V = (1/3)πr²h, the volume is V = (1/3) * 3.14 * (5)² * 10 = 261.67 cm³, rounded to 261.7 cm³.

Front

What is the significance of rounding in volume calculations?

Back

Rounding is important in volume calculations to provide a practical and understandable answer, especially in real-world applications.

Front

If a cone has a volume of 100 cm³ and a height of 5 cm, what is its radius?

Back

Using the formula V = (1/3)πr²h, rearranging gives r = sqrt((3V)/(πh)). Plugging in the values gives r = sqrt((3*100)/(3.14*5)) ≈ 3.18 cm.