Volume of a Cone

Front

What is the formula for the volume of a cone?

Back

V = (1/3)π r²h

Front

How do you calculate the volume of a cone with a radius of 3 cm and a height of 5 cm?

Back

V = (1/3)π (3)²(5) = 15π cm³ ≈ 47.12 cm³

Front

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

Back

V = (1/3)π (4)²(9) = 48π in³ ≈ 150.8 in³

Front

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

Back

The volume increases by a factor of 4, since V = (1/3)π (r²)(h).

Front

What is the volume of a cone with a radius of 2 m and a height of 3 m?

Back

V = (1/3)π (2)²(3) = 12/3π m³ = 4π m³ ≈ 12.57 m³

Front

Find the volume of a cone with a radius of 5 cm and a height of 10 cm.

Back

V = (1/3)π (5)²(10) = (1/3)π (25)(10) = (250/3)π cm³ ≈ 261.8 cm³

Front

What is the relationship between the radius and height in the volume formula for a cone?

Back

The volume of a cone is directly proportional to both the square of the radius and the height.

Front

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

Back

Look at the third decimal place; if it's 5 or more, round up the second decimal place.

Front

What is the volume of a cone with a radius of 6 inches and a height of 4 inches?

Back

V = (1/3)π (6)²(4) = (1/3)π (36)(4) = 48π in³ ≈ 150.8 in³

Front

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

Back

Using V = (1/3)π r²h, solve for r: r = sqrt((3V)/(πh)) = sqrt((3*100)/(π*5)) ≈ 3.98 cm.