Question

A conical hoe is drilled in a circular cylinder of height 12 cm and base radius 5 cm.The height and the base radius of the cone are also the same.Find the whole surface and volume of the remaining cylinder.

Answer 1

Answer:

_{Height of the cylinder = 12 cm, base radius = 5 cm
Height of the cone = 12 cm, base radius = 5 cm}

_{Surface area of the solid thus formed = Surface area of the cylinder + surface area of cone + area of the base of cylinder}

_{Surface area of the cone = $\pi rl$}

_{Slant height, $l=\sqrt{h^2+r^2}=\sqrt{{12}^2+5^2}=\sqrt{169}=13cm$}

_{Surface area of the solid thus formed = Surface area of the cylinder + surface area of cone + area of the base of cylinder}

_{$=2\pi rh+\pi rl+\pi r^2$}

_{$=\pi r(2h+l+r)$}

_{$=\pi \times 5(2\times 12+13+5)=\pi \times 5\times 42=210\pi c{m}^2$}

_{Thus surface area formed = $210\pi c{m}^2$}