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The students of a school were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard.Each penholder was to be radius of 3cm and height 10.5 cm. The school was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be brought for the competition. Assume: pi = 22/7

User Cartier
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Recall the surface area for the following figures.


\begin{gathered} \text{Cylinder}=2\pi rh+2\pi r^2 \\ \\ \text{The term }2\pi r^2\text{ includes a cover both the top and bottom of the cylinder} \\ \text{Since we will be using only the bottom modify the formula such that it only} \\ \text{includes the bottom part} \\ \\ \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \end{gathered}

Given that

height = h = 10.5 cm

radius = r = 3 cm

π = 22/7

Substitute the following given and we have the surface area for the pen holder


\begin{gathered} \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \\ \text{Pen Holder Surface Area}=2((22)/(7))(3\operatorname{cm})(10.5\operatorname{cm})+((22)/(7))(3\operatorname{cm})^2 \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+((22)/(7))(9\operatorname{cm}) \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+(198)/(7)\operatorname{cm} \\ \text{Pen Holder Surface Area}=(1584)/(7)\operatorname{cm}^2 \end{gathered}

Now that we have the surface area, multiply it by 35 since there are 35 competitors in the competition


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User Prabhat Mishra
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