Volume of a Cone

Front

What is the formula for the volume of a cone?

Back

Volume = (1/3) × π × r² × h, where r is the radius and h is the height.

Front

What does π (pi) represent in geometry?

Back

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

Front

If the radius of a cone is doubled, how does the volume change?

Back

The volume increases by a factor of 4, since volume is proportional to the square of the radius.

Front

What is the volume of a cone with a radius of 3 cm and a height of 4 cm?

Back

Volume = (1/3) × π × (3)² × (4) = 12π cm³ ≈ 37.7 cm³.

Front

How do you round a decimal 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 5 inches and a height of 12 inches?

Back

Volume = (1/3) × π × (5)² × (12) = 100π in³ ≈ 314.2 in³.

Front

What is the relationship between the height and volume of a cone?

Back

The volume of a cone is directly proportional to its height; if height increases, volume increases.

Front

What is the volume of a cone with a radius of 7 mm and a height of 10 mm?

Back

Volume = (1/3) × π × (7)² × (10) = 163.3 mm³.

Front

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

Back

Using the formula, r = √((3 × Volume) / (π × h)) = √((3 × 150) / (π × 10)) ≈ 4.4 cm.

Front

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

Back

Volume = (1/3) × π × (4)² × (9) = 48π m³ ≈ 150.8 m³.