Question

Can you please help me out with a question

Answer 1

The formula to find the lateral surface area of a hemisphere is

$\begin{gathered} \text{LSA}_{\text{hemisphere}}=2\pi r^2 \\ \text{ Where r is the radius of the hemisphere} \end{gathered}$

So, in this case, you have

$\begin{gathered} r=1in \\ \text{Because} \\ \text{radius}=\frac{\text{diameter}}{2} \\ \text{radius=}\frac{2in}{2} \\ \text{radius }=1in \end{gathered}$$\begin{gathered} \text{LSA}_{\text{hemisphere}}=2\pi r^2 \\ \text{LSA}_{\text{hemisphere}}=2\pi(1in)^2 \\ \text{LSA}_{\text{hemisphere}}=2\pi\cdot1in^2 \\ \text{LSA}_{\text{hemisphere}}=2\pi in^2 \end{gathered}$

Now, the formula to find the total surface area of a hemisphere is

$\begin{gathered} \text{TSA}_{\text{hemisphere}}=3\pi r^2 \\ \text{ Where r is the radius of the hemisphere} \end{gathered}$

So, you have

$\begin{gathered} \text{TSA}_{\text{hemisphere}}=3\pi r^2 \\ \text{TSA}_{\text{hemisphere}}=3\pi(1in)^2 \\ \text{TSA}_{\text{hemisphere}}=3\pi\cdot1in^2 \\ \text{TSA}_{\text{hemisphere}}=3\pi in^2 \end{gathered}$

Finally, the formula to find the volume of the hemisphere is

$V_{\text{hemisphere}}=\frac{1}{2}\cdot\frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3$

So, you have

$\begin{gathered} V_{\text{hemisphere}}=\frac{2}{3}\pi r^3 \\ V_{\text{hemisphere}}=\frac{2}{3}\pi(1in)^3 \\ V_{\text{hemisphere}}=\frac{2}{3}\pi\cdot1in^3 \\ V_{\text{hemisphere}}=\frac{2}{3}\pi in^3 \end{gathered}$