Question

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.
a1 = 2π×6×35 = 420π m²
a2 = 2π×6² = 72π m²
420π + 72π = 492π
a = 492×π = 1545.66228 = 1545.7 m²
b. bill wants to paint the silo. each can of paint covers approximately 37 square metres of area. estimate how many cans of paint he will need to paint the silo.

Explanation:

Step1: Calculate lateral surface area

The formula for the lateral - surface area of a cylinder $A_{l}=2\pi rh$. Given $r = \frac{d}{2}=\frac{12}{2}=6$ m and $h = 35$ m. So $A_{l}=2\pi\times6\times35 = 420\pi$ m².

Step2: Calculate base and top area

The formula for the area of the two bases of a cylinder $A_{b}=2\pi r^{2}$. Substituting $r = 6$ m, we get $A_{b}=2\pi\times6^{2}=72\pi$ m².

Step3: Calculate total surface area

The total surface area $A=A_{l}+A_{b}=420\pi + 72\pi=492\pi$ m². Using $\pi\approx3.14159$, $A = 492\times3.14159\approx1545.7$ m².

Step4: Calculate number of paint - cans

To find the number of paint - cans $n$, we use the formula $n=\frac{A}{37}$. Substituting $A\approx1545.7$ m², we get $n=\frac{1545.7}{37}\approx41.8$. Since we can't buy a fraction of a can, we need to round up. So $n = 42$ cans.

Answer:

a. $1545.7$ m²
b. 42 cans