SOLUTION
Given the pyramid with a square base in the image, the following are the solution steps wo find the surface area.
Step 1: Describe the formula of the surface area of the pyramid
The pyramid consists of a square base and 4 triangles, therefore the surface area of the pyramid will be the area of the square base added to the areas of the 4 triangles.
Step 2: To get the surface area of the pyramid, we calculate the area of the square base
[tex]\begin{gathered} \text{For the square base} \\ \text{Area}=s^2,s=25\text{ f}eet \\ \text{Area}=25^2=625feet^2 \end{gathered}[/tex]Step 3: We calculate the area of the 4 triangles
[tex]\begin{gathered} \text{Area}_{\text{triangle}}=\frac{1}{2}bh,\text{ b=25}feet,h=32 \\ \text{Area}_{\text{triangle}}=\frac{1}{2}\times25\times32 \\ \text{Area}_{\text{triangle}}=25\times16=400feet^2 \\ \text{Area of 4 triangles will be 4}\times\text{Area}_{\text{triangle}} \\ \text{Area}_{\text{all traingles}}=4\times400 \\ \text{Area}_{\text{all traingles}}=1600feet^2 \end{gathered}[/tex]Step 4: Calculate the surface area by following the instruction in Step 1:
[tex]1600+625=2225feet^2[/tex]Hence, the surface area of the pyramid equals 2225 square feet.
Question b: Surface area of the metal soup can
The metal soup can has the shape of a cylinder, therefore the surface area will be:
[tex]\begin{gathered} SA=2\pi r^2+2\pi r^{}h,r=5,h=20\operatorname{cm} \\ SA=(2\times\pi\times5\times5)+(2\times\pi\times5\times20) \\ SA=157.0796327+628.3185307 \\ SA=785.3981634 \\ SA\approx785.39816\operatorname{cm} \end{gathered}[/tex]Hence, the surface area of the metal soup can equals 785.39816 square cm.
Question c: Surface area of the ice cream cone with an open top
It can be seen from the image that the height is missing from the cone.
Surafce area of a cone with an open top means we exclude the area of the circular surface:
[tex]\begin{gathered} SA=\pi rl,l=16.6\operatorname{cm},r=\frac{9.4}{2}=4.7\operatorname{cm} \\ SA=\pi\times4.7\times16.6 \\ SA=245.1070588 \\ SA\approx245.107\operatorname{cm} \end{gathered}[/tex]Hence, the surface area of the ice cream cone can equals 245.107 square cm.
