Volume and Surface Area Concepts

This video tutorial covers the calculation of volume and surface area for composite shapes, including prisms, cuboids, hemispheres, cones, and pyramids. It provides step-by-step solutions to exam-style questions, emphasizing the importance of understanding geometric properties and formulas. The tutorial also highlights the use of non-calculator methods and significant figures in calculations.

What is a composite shape?

• A shape that is always a sphere

• A shape with only one face

• A shape made of two or more simple shapes

• A shape that cannot be divided

Tags

CCSS.7.G.B.6

How do you find the volume of a prism?

• Add the area of all faces

• Divide the area of the base by the height

• Multiply the area of the base by the height

• Multiply the perimeter by the height

Tags

CCSS.7.G.B.6

In the orange juice carton example, what was the depth of the orange juice after the carton was tilted?

• 4 cm

• 10 cm

• 8 cm

• 6 cm

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the formula for the volume of a cone?

• 1/2 πr²h

• 1/3 πr²h

• πr²h

• 2/3 πr²h

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you calculate the volume of a hemisphere?

• Add the surface area of the base

• Multiply the radius by the height

• Use the formula for a cone

• Use the formula for a full sphere and divide by two

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

When calculating the surface area of a hemisphere, what must be added to the curved surface area?

• The area of the circular base

• The diameter of the hemisphere

• The volume of the hemisphere

• The height of the hemisphere

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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

• 4πr²

• 3πr²

• 2πr²

• πr²

Tags

CCSS.7.G.B.6

In the pyramid problem, what is the length of each side of the square base?

• 8 cm

• 6 cm

• 12 cm

• 10 cm

Tags

CCSS.6.G.A.4

How do you find the vertical height of a pyramid with a square base?

• Use the Pythagorean theorem

• Divide the base by the height

• Measure the slant height

• Multiply the base by the height

Tags

CCSS.HSG.GMD.A.3

What is the volume of a pyramid with a square base and height?

• Base area divided by height

• 1/2 base area times height

• Base area times height

• 1/3 base area times height

Tags

CCSS.HSG.GMD.A.3