Question

1. bill, a farmer, wants to paint his silo. the silo has a cylinder base and a half - spherical roof as shown in the diagram.

a. calculate the surface area of the silo to the nearest tenth of a square metre if the diameter of the base is 12 m and the height of the cylinder is 35 m.

Explanation:

Step1: Calculate the radius

The diameter $d = 12$ m, so the radius $r=\frac{d}{2}=\frac{12}{2}=6$ m.

Step2: Calculate the lateral - surface area of the cylinder

The formula for the lateral - surface area of a cylinder is $A_{l}=2\pi rh$. Substituting $r = 6$ m and $h = 35$ m, we get $A_{l}=2\pi\times6\times35=420\pi$ $m^{2}$.

Step3: Calculate the surface area of the half - sphere

The formula for the surface area of a sphere is $A_{s}=4\pi r^{2}$, so the surface area of a half - sphere is $A_{h}=\frac{1}{2}\times4\pi r^{2}=2\pi r^{2}$. Substituting $r = 6$ m, we get $A_{h}=2\pi\times6^{2}=72\pi$ $m^{2}$.

Step4: Calculate the total surface area of the silo

The total surface area $A = A_{l}+A_{h}=420\pi+72\pi=492\pi$ $m^{2}$.
Using $\pi\approx3.14159$, we have $A\approx492\times3.14159 = 1545.66228\approx1545.7$ $m^{2}$.

Answer:

$1545.7$ $m^{2}$