How do you convert diameter to radius?

To convert diameter to radius, divide the diameter by 2: $$r = \frac{d}{2}$$ .

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

First, find the radius: $$r = \frac{10}{2} = 5 \text{ cm}$$ . Then use the volume formula: $$V = \frac{1}{3} \times \text{π} \times (5)^2 \times 12 = 100\text{π} \text{ cm}^3 \text{ (approximately 314.2 cm}^3)$$ .

What is the formula for the lateral surface area of a cylinder?

The lateral surface area of a cylinder is given by: $$A = 2\text{π}rh$$ .

What is the formula for the total surface area of a cone?

The total surface area of a cone is given by: $$A = \text{π}r(r + l)$$ , where l is the slant height.

If a cone has a slant height of 10 cm and a radius of 6 cm, what is its total surface area?

Using the formula: $$A = \text{π}r(r + l) = \text{π} \times 6 \times (6 + 10) = 96\text{π} \text{ cm}^2 \text{ (approximately 301.6 cm}^2)$$ .

What is the volume of a cylinder with a height of 7 cm and a base radius of 3 cm?

Using the formula: $$V = \text{π} \times (3)^2 \times 7 = 63\text{π} \text{ cm}^3 \text{ (approximately 197.8 cm}^3)$$ .

What is the significance of the constant π in volume calculations?

The constant π (approximately 3.14) is crucial in calculations involving circles, as it relates the diameter of a circle to its circumference and area.

How do you find the height of a cylinder if you know its volume and base radius?

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

Resource Library

Math

Geometry

Volume And Surface Area Of Cones

Volume Of Cylinders And Cones

Volume of Cylinders and Cones

Flashcard

•

Mathematics

•

8th Grade

•

Practice Problem

•

Hard

•

CCSS

8.G.C.9, 7.G.B.4, HSG.C.A.2

Standards-aligned

Wayground Content

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15 questions

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FLASHCARD QUESTION

Front

What is the formula for the volume of a cylinder?

Back

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

FLASHCARD QUESTION

Front

What is the formula for the volume of a cone?

Back

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

FLASHCARD QUESTION

Front

How do you find the area of a circle?

Back

Tags

CCSS.7.G.B.4

FLASHCARD QUESTION

Front

What is the difference between radius and diameter?

Back

The radius is the distance from the center of the circle to any point on its circumference, while the diameter is twice the radius, extending from one side of the circle to the other through the center.

Tags

CCSS.HSG.C.A.2

FLASHCARD QUESTION

Front

If a cylinder has a radius of 3 cm and a height of 5 cm, what is its volume?

Back

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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