Volume of a Cone

Front

What is the formula for the volume of a cone?

Back

V = (1/3)πr²h

Front

If the radius of a cone is 10 inches and the height is 25 inches, what is the volume?

Back

2616.7 in³

Front

What does π (pi) represent in the volume formula?

Back

π is a mathematical constant approximately equal to 3.14, representing the ratio of a circle's circumference to its diameter.

Front

How do you calculate the volume of a cone with a diameter of 12 cm and a height of 8 cm?

Back

First, find the radius (r = diameter/2 = 6 cm). Then use the formula: V = (1/3)πr²h = (1/3)π(6)²(8) = 301.4 cm³.

Front

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

Back

The radius is half of the diameter (r = diameter/2).

Front

If a cone has a height of 6 inches and a radius of 5 inches, what is its volume?

Back

157 in³

Front

What units are used to measure the volume of a cone?

Back

Cubic units (e.g., in³, cm³, mm³).

Front

How do you round decimal answers to the nearest tenth?

Back

Look at the hundredths place; if it's 5 or more, round up the tenths place by one.

Front

What is the volume of a cone with a radius of 9 mm and a height of 35 mm?

Back

2967.3 mm³

Front

What is the significance of the factor (1/3) in the volume formula for a cone?

Back

It accounts for the fact that a cone occupies one-third the volume of a cylinder with the same base and height.