Calculating Surface Area and Volume of Composite Solids

Mrs. Kidman explains how to find the surface area and volume of composite shapes, which are combinations of multiple 3D solids. The video covers methods for calculating volume by either adding or subtracting the volumes of individual shapes, depending on their arrangement. It also includes practice problems and a detailed explanation of how to calculate the surface area, considering overlapping parts. The video emphasizes the importance of understanding the geometry of composite shapes and provides tips for using the Pythagorean theorem to find missing dimensions.

What defines a composite shape?

• A shape made from cutting one 3D solid out of another

• A shape consisting of more than one 3D solid combined

• A shape that changes form when viewed from different angles

• A shape that can be divided into two equal halves

Tags

CCSS.1.G.A.2

What is the formula to calculate the volume of a cylinder?

• Volume = pi * radius * height

• Volume = pi * radius^2 * height

• Volume = 2 * pi * radius * height

• Volume = 1/3 * pi * radius^2 * height

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you find the volume of a cylinder placed on top of a cube?

• Divide the volume of the cube by the cylinder

• Subtract the volume of the cylinder from the cube

• Multiply the volumes of the two shapes

• Add the volumes of the cylinder and the cube

Tags

CCSS.5.MD.C.5C

What is the volume formula for a pyramid?

• Volume = 1/3 * base area * height

• Volume = base area * height

• Volume = 1/2 * base area * height

• Volume = 2/3 * base area * height

Tags

CCSS.HSG.GMD.A.3

What is the formula for calculating the volume of a cone?

• Volume = 1/3 * pi * radius^2 * height

• Volume = 2 * pi * radius * height

• Volume = pi * radius^2 * height

• Volume = 1/2 * pi * radius^2 * height

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

When a cone is cut out from a pyramid, how do you find the composite volume?

• Divide the volume of the pyramid by the cone

• Multiply the volumes of both shapes

• Add the volumes of both shapes

• Subtract the volume of the cone from the pyramid

Tags

CCSS.5.MD.C.5C

How do you find the volume of a shape with a cylinder and a sphere combined?

• By subtracting the volume of the sphere from the cylinder

• By multiplying the volumes of the cylinder and the sphere

• By adding the volumes of the cylinder and the sphere

• By dividing the volume of the cylinder by the sphere

Tags

CCSS.5.MD.C.5C

How do you calculate the surface area of a composite shape?

• By subtracting the surface areas of the individual shapes

• By adding the surface areas of the individual shapes, considering overlaps

• By multiplying the surface areas of the individual shapes

• By dividing the surface area of one shape by the other

What role does the Pythagorean theorem play in calculating surface area of composite shapes?

• It has no role in calculating surface area

• It is used to find lengths necessary for surface area calculations

• It helps in finding the height of shapes for volume calculation

• It is used to calculate the volume of the shapes

Tags

CCSS.8.G.B.8

What is the correct approach when a part of a composite shape is not exposed?

• Exclude its surface area from the total calculation

• Multiply its surface area by two

• Include its surface area in the total calculation

• Divide its surface area by two

Tags

CCSS.6.G.A.4