What is the approximate value of $$\pi$$ ?

The approximate value of $$\pi$$ is 3.14.

What is the volume of a cone with a radius of 3 cm and a height of 5 cm?

Using the formula, $$V = \frac{1}{3} \pi (3)^2 (5) = \frac{1}{3} \pi (9)(5) = 15\pi \approx 47.12$$ cubic cm.

If the volume of a cone is 150.8 cm³, what could be its height if the radius is 3 cm?

Using the formula, rearranging gives $$h = \frac{3V}{\pi r^2} = \frac{3(150.8)}{\pi (3)^2} \approx 17.84$$ cm.

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

The volume of a cone is one-third the volume of a cylinder with the same base and height.

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

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

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

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

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

Using the formula, $$V = \frac{1}{3} \pi (2)^2 (3) = \frac{1}{3} \pi (4)(3) = 4\pi \approx 12.57$$ cubic inches.

If a cone has a volume of 268.08 inches³, what could be its height if the radius is 4 inches?

Using the formula, rearranging gives $$h = \frac{3V}{\pi r^2} = \frac{3(268.08)}{\pi (4)^2} \approx 25.5$$ inches.

What is the significance of the factor $$\frac{1}{3}$$ in the volume formula of a cone?

The factor $$\frac{1}{3}$$ indicates that the volume of a cone is one-third of the volume of a cylinder with the same base and height.

Volume of Cones Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the formula for the Volume of a Cone?

Back

2.

FLASHCARD QUESTION

Front

What does 'r' represent in the volume formula of a cone?

Back

'r' represents the radius of the base of the cone.

3.

FLASHCARD QUESTION

Front

What does 'h' represent in the volume formula of a cone?

Back

'h' represents the height of the cone.

4.

FLASHCARD QUESTION

Front

How do you calculate the radius from the diameter of a cone?

Back

5.

FLASHCARD QUESTION

Front

If a cone has a height of 4 inches and a diameter of 8 inches, what is the radius?

Back

6.

FLASHCARD QUESTION

Front

Calculate the volume of a cone with a radius of 4 inches and a height of 4 inches.

Back

7.

FLASHCARD QUESTION

Front

Back

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