What is the formula for the volume of a cylinder?

The volume of a cylinder is given by the formula: $$V = \text{π}r^2h$$ , where r is the radius and h is the height.

How do you calculate the height of a cone if the volume and radius are known?

Rearranging the volume formula $$V = \frac{1}{3}\text{π}r^2h$$ gives: $$h = \frac{3V}{\text{π}r^2}$$ .

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

Using the formula $$V = \frac{1}{3}\text{π}r^2h$$ , the volume is: $$V = \frac{1}{3}\text{π}(4)^2(6) = 32\text{π} \text{ cm}^3$$ .

What is the volume of a pyramid with a square base of side 4 cm and a height of 5 cm?

The base area is $$B = 4^2 = 16 \text{ cm}^2$$ . Thus, the volume is: $$V = \frac{1}{3}(16)(5) = \frac{80}{3} \text{ cm}^3$$ .

What is the effect of increasing the height of a cone on its volume?

Increasing the height of a cone while keeping the radius constant will increase the volume linearly, as volume is directly proportional to height: $$V \text{ (new)} = \frac{1}{3}\text{π}r^2h_{new}$$ .

What is the volume of a cone with a diameter of 10 cm and a height of 12 cm?

First, find the radius: r = 5 cm. Then, using the formula $$V = \frac{1}{3}\text{π}r^2h$$ , the volume is: $$V = \frac{1}{3}\text{π}(5)^2(12) = 100\text{π} \text{ cm}^3$$ .

What is the volume of a cylinder with a height of 10 cm and a base radius of 2 cm?

Using the formula $$V = \text{π}r^2h$$ , the volume is: $$V = \text{π}(2)^2(10) = 40\text{π} \text{ cm}^3$$ .

What is the volume of a cone with a base area of 25 cm² and a height of 3 cm?

Using the formula $$V = \frac{1}{3}Bh$$ , the volume is: $$V = \frac{1}{3}(25)(3) = 25 \text{ cm}^3$$ .

Volume of Pyramids and Cones Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the formula for the volume of a pyramid?

Back

2.

FLASHCARD QUESTION

Front

What is the formula for the volume of a cone?

Back

3.

FLASHCARD QUESTION

Front

How do you find the area of a circle?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

What is the volume of a pyramid with a base area of 20 cm² and a height of 9 cm?

Back

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