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

Using the formula: $$V = \frac{1}{3} \pi r^2 h$$ , the volume is: $$V = \frac{1}{3} \pi (3^2)(4) = 12\pi \approx 37.70 \text{ m}^3$$ .

What is the volume of a cylinder with a radius of 3 m and a height of 4 m?

Using the formula: $$V = \pi r^2 h$$ , the volume is: $$V = \pi (3^2)(4) = 36\pi \approx 113.10 \text{ m}^3$$ .

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

The volume of the cone is one-third of the volume of the cylinder: $$V_{cone} = \frac{1}{3} V_{cylinder}$$ .

What is the volume of a composite solid made of a cylinder and a cone on top, both with a radius of 3 m and height of 4 m?

Calculate the cylinder's volume: $$V_{cylinder} = 36\pi$$ and the cone's volume: $$V_{cone} = 12\pi$$ . Total volume: $$V_{total} = 36\pi + 12\pi = 48\pi \approx 150.80 \text{ m}^3$$ .

What is the volume of a cone with a diameter of 8 inches and a height of 8 inches?

First, find the radius: r = 4 inches. Then, use the formula: $$V = \frac{1}{3} \pi (4^2)(8) = \frac{128}{3}\pi \approx 134.04 \text{ in}^3$$ .

What is the volume of a cylinder with a diameter of 8 inches and a height of 8 inches?

First, find the radius: r = 4 inches. Then, use the formula: $$V = \pi (4^2)(8) = 128\pi \approx 402.12 \text{ in}^3$$ .

Which is a better value: a cone or a cylinder with the same dimensions?

The cylinder has a greater volume than the cone, making it a better value for the same height and diameter.

Volume Practice: Comparing and Composite Solids Flashcards

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14 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 volume of a cylinder?

Back

3.

FLASHCARD QUESTION

Front

How do you compare the volumes of a cone and a cylinder with the same base and height?

Back

4.

FLASHCARD QUESTION

Front

What is a composite solid?

Back

A composite solid is a three-dimensional shape that is made up of two or more simple shapes, such as cones, cylinders, and prisms.

5.

FLASHCARD QUESTION

Front

How do you find the volume of a composite solid?

Back

To find the volume of a composite solid, calculate the volume of each simple shape separately and then sum them up.

6.

FLASHCARD QUESTION

Front

What is the volume of a rectangular prism?

Back

7.

FLASHCARD QUESTION

Front

What is the volume of a shoe box with dimensions 12 cm x 7 cm x 5 cm?

Back

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