Question

Not sure on how to do this. Could really use some help. (There is 2 parts to this question)

Answer 1

The figure attached is composed of a cylinder and an sphere. Then:

Surface Area = Total Area of the Sphere + Side Area of the Cylinder.

Hence:

`\begin{gathered} A_(sphere)=4πr^2 \\ A_(sphere)=4*\pi*8^2 \\ A_(sphere)=804.25cm^2 \end{gathered}`

Now, the side area of the cylinder:

`\begin{gathered} SA_(cylinder)=2*π* r* h \\ SA_(cylinder)=2*π*8*12.5 \\ SA_(cylinder)=628.32cm^2 \end{gathered}`

Finally:

`SA=804.25+628.32=1432.57cm^2`

ANSWER

The surface area is 1432.6 cm²

Now, to find the volume:

Total Volume = Volume of the Sphere + Volume of the Cylinder

Volume of the Sphere:

`\begin{gathered} V_(sphere)=(4)/(3)πr³ \\ V_(sphere)=(4)/(3)\pi*8^3=2144.66cm^3 \end{gathered}`

Volume of the Cylinder:

`\begin{gathered} V_(cylinder)=πr²h \\ V_(cylinder)=π*8^2*12.5=2513.27cm^3 \end{gathered}`

Finally:

`V=2144.66+2513.27=4657.93cm^3`

ANSWER

The volume is 4657.9cm³