Find the volume and surface area of the composite figure. give your answer in terms of π.

Part 1) The volume of the composite figure is

Part 2) The surface area of the composite figure is

Step-by-step explanation:

Part 1) Find the volume of the composite figure

we know that

The volume of the figure is equal to the volume of a cone plus the volume of a hemisphere

Find the volume of the cone

The volume of the cone is equal to

we have

Applying Pythagoras Theorem find the value of h

substitute

Find the volume of the hemisphere

The volume of the hemisphere is equal to

we have

substitute

therefore

The volume of the composite figure is equal to

Part 2) Find the surface area of the composite figure

we know that

The surface area of the composite figure is equal to the lateral area of the cone plus the surface area of the hemisphere

Find the lateral area of the cone

The lateral area of the cone is equal to

we have

substitute

Find the surface area of the hemisphere

The surface area of the hemisphere is equal to

we have

substitute

Find the surface area of the composite figure

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