Exploring Composite Solids: Volume and Surface Area

This video tutorial covers two examples of calculating the volume and surface area of composite solids. In Example A, the volume of a parallelogram-based prism with a cylinder removed is calculated by subtracting the cylinder's volume from the prism's volume. In Example B, the surface area of a composite solid consisting of a cylinder and a hemisphere is determined by calculating the areas of the bottom circle, lateral surface, and half-sphere, while excluding the top circle of the cylinder.

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

• Volume = (1/3) x Base Area x Height

• Volume = 2 x Base Area + Height

• Volume = Base Area x Height

• Volume = Length x Width x Height

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CCSS.7.G.B.6

What is the base area of the parallelogram used in the prism?

• 625 cm²

• 250 cm²

• 500 cm²

• 1250 cm²

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CCSS.7.G.B.6

How do you find the radius of a cylinder if its diameter is given as 8 cm?

• Radius = 4 cm

• Radius = 16 cm

• Radius = 2 cm

• Radius = 8 cm

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CCSS.7.G.B.4

What is the volume of the cylinder subtracted from the prism?

• 18,750 cm³

• 18,750 - 480π cm³

• 480π cm³

• 18,270 cm³

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CCSS.5.MD.C.5C

What is the significance of subtracting the cylinder's volume from the prism's volume?

• To calculate the total volume of the composite solid

• To find the volume of the space between them

• To adjust for measurement errors

• To determine the volume of the cylinder only

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CCSS.5.MD.C.5C

What components are considered when calculating the surface area of the composite solid?

• Circle, Rectangle, Sphere

• Circle, Lateral Surface, Hemisphere

• Rectangle, Triangle, Hemisphere

• Square, Lateral Surface, Quarter Sphere

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CCSS.5.MD.C.5C

How is the lateral surface area of the cylinder calculated?

• 2πrh

• πr²h

• 2πr²

• πr² + 2πrh

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

• 2πr²

• πr²

• 4πr²

• πr³

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the total surface area of the composite solid?

• 264π inches²

• 156π inches²

• 72π inches²

• 36π inches²

Why is the top circle area not included in the surface area calculation of the composite solid?

• Because it is covered by the hemisphere

• Because it does not contribute to the external surface area

• All of the above

• Because it is considered part of the hemisphere