Respuesta :
We are asked to calculate the surface area of the objects using the following formula
[tex]SA=2\times(\pi\times r^2)+(\pi\times d\times h)[/tex]Where r is the radius, d is the diameter, and h is the height of the circular cylinder.
Part a)
The diameter (d) is 2.5 cm
The height (h) is 10 cm
The radius is half of the diameter
[tex]r=\frac{d}{2}=\frac{2.5}{2}=1.25\; cm[/tex]Let us substitute the given values into the formula
[tex]\begin{gathered} SA=2\times(\pi\times r^2)+(\pi\times d\times h) \\ SA=2\times(\pi\times1.25^2)+(\pi\times2.5\times10) \\ SA=2\times1.5625\pi+25\pi \\ SA=3.125\pi+25\pi \\ SA=28.125\pi \\ SA=88.36\; cm^2 \end{gathered}[/tex]The surface area of the object is 88.36 cm^2
Part b)
The diameter (d) is 5 cm
The height (h) is 7 cm
The radius is half of the diameter
[tex]r=\frac{d}{2}=\frac{5}{2}=2.5\; cm[/tex]Let us substitute the given values into the formula
[tex]\begin{gathered} SA=2\times(\pi\times r^2)+(\pi\times d\times h) \\ SA=2\times(\pi\times2.5^2)+(\pi\times5\times7) \\ SA=2\times(6.25\pi)+(35\pi) \\ SA=12.5\pi+35\pi \\ SA=47.5\pi \\ SA=149.23\; cm^2 \end{gathered}[/tex]The surface area of the object is 149.23 cm^2
