Question

Geometry Math Question.*Please put the answers in simplified radical form*

Answer 1

Solution

Part a

For this case we can find the individual areas for each surface and we have:

$A_1=2\pi(8cm)^2=402.124\operatorname{cm}^2$$A_2=2\pi r(r+h)=2\pi(8)(8+15)=1156.106\operatorname{cm}^2$$A_3=\pi(8^2)+\pi(8)\cdot(17)=628.319\operatorname{cm}^2$

Then the total surface area is:

$A=A_1+A_2+A_3=2186.549\operatorname{cm}^2$

A simplified form would be:

$A=696\pi$

Part b

$V_1=\frac{2}{3}\pi(8\operatorname{cm})^3=1072.331\operatorname{cm}^3$$V_2=\pi(8^2)(15)=3015.929\operatorname{cm}^3$$V_3=\frac{1}{3}\pi(8^2)\cdot15=1005.310\operatorname{cm}^3$

Then the total volume is:

$V=V_1+V_2+V_2=5093.570\operatorname{cm}^3$$V=\frac{4864}{3}\pi$