Solution
Step 1
Determine the number of shapes in figure 1
Figure 1 is made up of a cone and a hemisphere
Step 2
Write out the expression for the area of a cone and a hemisphere
[tex]\begin{gathered} \text{The area of a cone = }\pi\times r\times l \\ \text{The area of a hemisphere = 2}\times\pi\times r^2 \end{gathered}[/tex]Where
pi =3.14
r = 7 inches
l = 15 inches
Step 3
Substitute in the values and find the area of the shape
[tex]\begin{gathered} \text{Total area of the shape is given as} \\ \text{area of cone + area }of\text{ hemisphere} \\ =\text{ 2 x 3.14 }\times7^2+(3.14\text{ }\times7\times15) \\ =\text{ 307.72 + 329.7} \\ =637.42inch^2\text{ to 2 decimal places} \end{gathered}[/tex]Area = 637.42 square inches
Step 4
Determine the number of shapes in figure 2
Figure 2 is made up of a cone and a cylinder
Step 5
Write an expression for the area of a cylinder
[tex]\text{The area of a cylinder = 2}\times\pi\times r\times h\text{ + }\pi\times r^2[/tex]where h = 13yards
radius(r) = 11/2 = 5.5inches
l = ?
To find l, the slant height we use the Pythagoras theorem
so that
[tex]\begin{gathered} l^2=11^2+9^2 \\ l^2=202 \\ l\text{ =}\sqrt[]{202} \\ l\text{ = 14.2126704 in} \end{gathered}[/tex]Step 6
Substitute in the values and find the area of the shape
[tex]\begin{gathered} \text{Area of figure 2 is given as} \\ \pi\times r\times l\text{ + (2}\times\pi\times r\times h\text{ + }\pi\times r^2) \\ (3.14\text{ }\times\text{ 5.5}\times14.2126704)+((2\times3.14\times5.5\times13)+\text{ (3.14 }\times5.5^2) \end{gathered}[/tex][tex]\begin{gathered} 245.4528179+94.985+449.02=789.4578179Inches^2 \\ To\text{ 2 decimal places }\approx789.46inches^2 \end{gathered}[/tex]Area = 789.46 square inches