Volume of Spheres, Cones, and Cylinders and Surface Area

Front

What is the formula for the volume of a sphere?

Back

The volume V of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula V = (1/3)πr²h, where r is the radius of the base and h is the height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the formula for the surface area of a sphere?

Back

The surface area A of a sphere is given by the formula A = 4πr², where r is the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

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

Back

The surface area A of a cylinder is given by the formula A = 2πr(h + r), where r is the radius and h is the height.

Front

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

Back

The surface area A of a cone is given by the formula A = πr(r + l), where r is the radius and l is the slant height.

Front

If the radius of a sphere is 5 m, what is its volume?

Back

Using the formula V = (4/3)πr³, the volume is approximately 523.6 m³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If a cylinder has a radius of 3 ft and a height of 10 ft, what is its volume?

Back

Using the formula V = πr²h, the volume is approximately 94.25 ft³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the height of a cylinder with a base area of 153.86 ft² and a volume of 615.44 ft³?

Back

The height h can be found using the formula h = V / A. Here, h = 615.44 ft³ / 153.86 ft² = 4 ft.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the total surface area of a cylinder with a radius of 3 cm and a height of 10 cm?

Back

Using the formula A = 2πr(h + r), the total surface area is approximately 245.04 cm².