Question

Find the surface area of each figure. Round answer to two decimal places. use 3.14 for pi

Answer 1

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

`\begin{gathered} \text{The area of a cone = }\pi* r* l \\ \text{The area of a hemisphere = 2}*\pi* r^2 \end{gathered}`

Where

pi =3.14

r = 7 inches

l = 15 inches

Step 3

Substitute in the values and find the area of the shape

`\begin{gathered} \text{Total area of the shape is given as} \\ \text{area of cone + area }of\text{ hemisphere} \\ =\text{ 2 x 3.14 }*7^2+(3.14\text{ }*7*15) \\ =\text{ 307.72 + 329.7} \\ =637.42inch^2\text{ to 2 decimal places} \end{gathered}`

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

`\text{The area of a cylinder = 2}*\pi* r* h\text{ + }\pi* r^2`

where h = 13yards

radius(r) = 11/2 = 5.5inches

l = ?

To find l, the slant height we use the Pythagoras theorem

so that

`\begin{gathered} l^2=11^2+9^2 \\ l^2=202 \\ l\text{ =}\sqrt[]{202} \\ l\text{ = 14.2126704 in} \end{gathered}`

Step 6

Substitute in the values and find the area of the shape

`\begin{gathered} \text{Area of figure 2 is given as} \\ \pi* r* l\text{ + (2}*\pi* r* h\text{ + }\pi* r^2) \\ (3.14\text{ }*\text{ 5.5}*14.2126704)+((2*3.14*5.5*13)+\text{ (3.14 }*5.5^2) \end{gathered}`
`\begin{gathered} 245.4528179+94.985+449.02=789.4578179Inches^2 \\ To\text{ 2 decimal places }\approx789.46inches^2 \end{gathered}`

Area = 789.46 square inches