Answer:
Part 1) The volume of the composite figure is [tex]620.7\pi\cm^{3}[/tex]
Part 2) The surface area of the composite figure is [tex]273\pi\ cm^{2}[/tex]
[tex]V=620.7\pi\cm^{3}, S=273\pi\ cm^{2}[/tex]
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
[tex]V=\frac{1}{3} \pi r^{2} h[/tex]
we have
[tex]r=7\ cm[/tex]
Applying Pythagoras Theorem find the value of h
[tex]h^{2}=25^{2} -7^{2} \\ \\h^{2}= 576\\ \\h=24\ cm[/tex]
substitute
[tex]V=\frac{1}{3} \pi (7)^{2} (24)[/tex]
[tex]V=392 \pi\cm^{3}[/tex]
Find the volume of the hemisphere
The volume of the hemisphere is equal to
[tex]V=\frac{4}{6}\pi r^{3}[/tex]
we have
[tex]r=7\ cm[/tex]
substitute
[tex]V=\frac{4}{6}\pi (7)^{3}[/tex]
[tex]V=228.7\pi\cm^{3}[/tex]
therefore
The volume of the composite figure is equal to
[tex]392 \pi\cm^{3}+228.7\pi\cm^{3}=620.7\pi\cm^{3}[/tex]
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
[tex]LA=\pi rl[/tex]
we have
[tex]r=7\ cm[/tex]
[tex]l=25\ cm[/tex]
substitute
[tex]LA=\pi(7)(25)[/tex]
[tex]LA=175\pi\ cm^{2}[/tex]
Find the surface area of the hemisphere
The surface area of the hemisphere is equal to
[tex]SA=2\pi r^{2}[/tex]
we have
[tex]r=7\ cm[/tex]
substitute
[tex]SA=2\pi (7)^{2}[/tex]
[tex]SA=98\pi\ cm^{2}[/tex]
Find the surface area of the composite figure
[tex]175\pi\ cm^{2}+98\pi\ cm^{2}=273\pi\ cm^{2}[/tex]
