Calculating Volume and Surface Area of 3D Shapes

The video tutorial covers the calculation of surface area and volume for cylinders, cones, and spheres. It begins with the surface area of a cylinder, explaining the formula and solving example problems. The tutorial then moves on to the volume of a cylinder, followed by the volume of a cone, emphasizing the need to memorize the formula. The surface area and volume of a sphere are also discussed, with a note on the use of calculus for derivation. The tutorial concludes with practical examples to reinforce understanding.

What formula is used to calculate the surface area of the top or bottom of a cylinder?

• 2πrh

• 2πr^2

• πr^2h

• πr^2

How do you calculate the surface area of the curved part of a cylinder?

• πrh

• 2πr^2

• πr^2

• 2πrh

What is the formula for the volume of a cylinder?

• 2πr^2

• 2πrh

• πr^2h

• πr^2 + 2πrh

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How is the radius calculated if the diameter is given?

• Radius = Diameter^2

• Radius = Diameter / 2

• Radius = Diameter * 2

• Radius = π * Diameter

Tags

CCSS.7.G.B.4

What is the volume formula for a cone?

• πr^3

• 1/3πr^2h

• πr^2h

• 2/3πr^2h

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What factor differentiates the volume of a cone from that of a cylinder?

• 1/4

• 1/3

• 2/3

• 1/2

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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

• πr^3

• 2πr^2

• πr^2

• 4πr^2

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How does the formula for the surface area of a sphere relate to its radius?

• It is directly proportional to the square of the radius.

• It is inversely proportional to the square of the radius.

• It is directly proportional to the radius.

• It is inversely proportional to the radius.

What is the volume formula for a sphere?

• πr^3

• 4/3πr^3

• πr^2h

• 2/3πr^3

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you calculate the radius from the diameter?

• Multiply the diameter by π

• Divide the diameter by 2

• Square the diameter

• Multiply the diameter by 2

Tags

CCSS.7.G.B.4