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A bat manufacturing company made a huge bat for charity and got it signed by world cup winning team. The dimensions of the bat which is in the form of a cuboid with a cylindrical handle at the top are as follows : length = $2$ m, width = $0.5$ m, thickness = $0.1$ m, diameter of cylindrical part = $0.1$ m, height of cylindrical part = $0.7$ m. Find the volume of wood used in the bat. Also, find the total surface area of the wooden bat.
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Radius of cylindrical part = $\frac{0.1}{2}$ m or $\frac{1}{20}$ m. Volume of wood = Volume of cuboid + volume of cylinder = $2 \times 0.5 \times 0.1 + \frac{22}{7} \times \frac{0.1}{2} \times \frac{0.1}{2} \times 0.7 = \frac{211}{2000}$ or $0.1055$ m$^3$. Total surface area of bat = TSA of cuboid + CSA of cylinder = $2(2 \times 0.5 + 0.5 \times 0.1 + 0.1 \times 2) + 2 \times \frac{22}{7} \times \frac{0.1}{2} \times 0.7 = \frac{5}{2} + \frac{11}{50} = \frac{68}{25}$ or $2.72$ m$^2$.