Solution
Step 1
Write the expression for the surface area of a hemisphere
[tex]\text{Surface area of a hemisphere (A}_1)=\text{ 2}\times\pi\times r^2[/tex]Where
π = 3.14
r= 4.5 inches
Step 2
Write the expression for the surface area of a cone
[tex]\begin{gathered} \text{Surface area of a cone (A}_2)\text{ = }\pi\times r\times l \\ l\text{ = slant height } \\ To\text{ find l we use Pythagoras theorem} \\ \end{gathered}[/tex]Step 3
Draw the triangle and find l using Pythagoras theorem
From the diagram
l²= 4.5²+10²
l =√(100 + 20.25)
l= √120.25
l = 10.97 inches
Step 4
Find the area of the hemisphere and cone by substitution and calculation
[tex]\begin{gathered} A_{1\text{ }}=2\times3.14\times4.5^2 \\ A_1=127.17in^2 \\ A_2=\text{ 3.14 }\times\text{ 4.5 }\times\text{ 10.97} \\ A_2=155.0061in^2 \end{gathered}[/tex]Step 5
Find the total surface area of the shape
[tex]\text{The total surface area of the shape = A}_1+A_2=127.17+155.0061=282.18in^2\text{ approxi}mately[/tex]Hence the total area of the shape = 282.2 in²
Option F is the right answer