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Nataliya [291]
3 years ago
13

Find the volume and surface area of the composite figure. Give your answer in terms of π. HELP ASAP!!

Mathematics
1 answer:
NARA [144]3 years ago
4 0

Answer:

Part 1) The volume of the composite figure is 620.7\pi\cm^{3}

Part 2) The surface area of the composite figure is 273\pi\ cm^{2}

V=620.7\pi\cm^{3}, S=273\pi\ cm^{2}

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

<em>Find the volume of the cone</em>

The volume of the cone is equal to

V=\frac{1}{3} \pi r^{2} h

we have

r=7\ cm

Applying Pythagoras Theorem find the value of h

h^{2}=25^{2} -7^{2} \\ \\h^{2}= 576\\ \\h=24\ cm

substitute

V=\frac{1}{3} \pi (7)^{2} (24)

V=392 \pi\cm^{3}

<em>Find the volume of the hemisphere</em>

The volume of the hemisphere is equal to

V=\frac{4}{6}\pi r^{3}

we have

r=7\ cm

substitute

V=\frac{4}{6}\pi (7)^{3}

V=228.7\pi\cm^{3}

therefore

The volume of the composite figure is equal to

392 \pi\cm^{3}+228.7\pi\cm^{3}=620.7\pi\cm^{3}

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

<em>Find the lateral area of the cone</em>

The lateral area of the cone is equal to

LA=\pi rl

we have

r=7\ cm

l=25\ cm

substitute

LA=\pi(7)(25)

LA=175\pi\ cm^{2}

<em>Find the surface area of the hemisphere</em>

The surface area of the hemisphere is equal to

SA=2\pi r^{2}

we have

r=7\ cm

substitute

SA=2\pi (7)^{2}

SA=98\pi\ cm^{2}

Find the surface area of the composite figure

175\pi\ cm^{2}+98\pi\ cm^{2}=273\pi\ cm^{2}

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