What is the base area of a cone with a radius of 2 cm?

The base area of a cone is given by the formula: $$\text{Base Area} = \text{π} \times r^2$$ . For r = 2 cm, the base area is $$\text{Base Area} = \text{π} \times 2^2 = 4\text{π} \text{ cm}^2$$ .

How many times greater is the volume of a cylinder than that of a cone with the same base and height?

The volume of a cylinder is three times greater than that of a cone with the same base and height.

What is the volume of a cone with a diameter of 6 cm and a height of 9 cm?

Using the formula $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ , the volume is $$V = \frac{1}{3} \times \text{π} \times (3)^2 \times 9 = 27\text{π} \text{ cm}^3$$ .

What is the volume of a pyramid with a triangular base of area 10 cm² and height 5 cm?

Using the formula $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ , the volume is $$V = \frac{1}{3} \times 10 \times 5 = \frac{50}{3} \text{ cm}^3$$ .

What is the volume of a cone if its height is 10 cm and the radius is 4 cm?

Using the formula $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ , the volume is $$V = \frac{1}{3} \times \text{π} \times (4)^2 \times 10 = \frac{160\text{π}}{3} \text{ cm}^3$$ .

What is the volume of a square pyramid with a base area of 16 cm² and a height of 9 cm?

Using the formula $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ , the volume is $$V = \frac{1}{3} \times 16 \times 9 = 48 \text{ cm}^3$$ .

If a cone has a height of 12 cm and a radius of 3 cm, what is its volume?

Using the formula $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ , the volume is $$V = \frac{1}{3} \times \text{π} \times (3)^2 \times 12 = 36\text{π} \text{ cm}^3$$ .

volume of cones and pyramids Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the formula for the volume of a cone?

Back

2.

FLASHCARD QUESTION

Front

What is the formula for the volume of a pyramid?

Back

3.

FLASHCARD QUESTION

Front

How does the volume of a pyramid compare to a prism with the same base area and height?

Back

The volume of a pyramid is one-third the volume of a prism with the same base area and height.

4.

FLASHCARD QUESTION

Front

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

Back

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

5.

FLASHCARD QUESTION

Front

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

Back

If the radius is doubled, the volume increases by a factor of four, since volume is proportional to the square of the radius.

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

What is the volume of a square pyramid with a base side of 5 cm and a height of 12 cm?

Back

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