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=}(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}}=(1)/(2)\cdot(4)/(3)\pi r^3=(2)/(3)\pi r^3`

So, you have

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