From a solid cylinder whose height is 2.4 cm and diameter of 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.

Question

Infinity Learn · Accepted Answer

The figure of the solid can be created as per the given information as shown below.As the conical cavity is of the same height and diameter has been hollowed out, it can be seen that one of the bases of the cylinder is not included in the total surface area of the solid.TSA of the remaining solid $$=$$ CSA of the cylindrical part $$+$$ CSA of conical part $$+$$ Area of one cylindrical baseLet us find the area of the remaining solid by using formulae; CSA of $$cylinder=$$ $$2$$$$π$$rhArea of the base of the cylinder $$=$$ π$$r2$$, where r and h are radius and height of the cylinder respectively.CSA of the cone $$=$$ πrlSlant height of the cone, l $$=$$ √[$$r2$$ $$+$$ $$h2$$]where r, h and l are radius, height and slant height of the cone respectively.Height of the cylinder $$=$$ Height of the cone $$=$$ h $$=$$ $$2.4$$ cmDiameter of the cylinder $$=$$ diameter of the cone $$=$$ d $$=$$ $$1.4$$ cmRadius of the cylinder $$=$$ radius of the cone $$=$$ r $$=$$ d $$/$$ $$2$$ $$=$$ $$1.4$$ $$/$$ $$2$$ cm $$=$$ $$0.7$$ cmSlant height of the cone, l $$=$$ √[$$r2$$ $$+$$ $$h2$$]l $$=$$ √[$$(0.7$$ $$cm)2$$ $$+$$ $$(2.4$$ $$cm)2$$]$$=$$ √[$$0.49$$ $$cm2$$ $$+$$ $$5.76$$ $$cm2$$]$$=$$ √[$$6.25$$ $$cm2$$]$$=$$ $$2.5$$ cmTSA of the remaining solid $$=$$ CSA of the cylindrical part $$+$$ CSA of conical part $$+$$ Area of one cylindrical $$base=$$ $$2$$$$π$$rh $$+$$ πrl $$+$$ π$$r2=$$ πr $$(2h$$ $$+$$ l $$+$$ $$r)=$$ $$22/7$$ × $$0.7$$ cm × $$(2$$ × $$2.4$$ cm $$+$$ $$2.5$$ cm $$+$$ $$0.7$$ $$cm)=$$ $$2.2$$ cm × $$8$$ $$cm=$$ $$17.6$$ $$cm2Hence$$, the total surface area of the remaining solid to the nearest $$cm2$$ is $$18$$ $$cm2$$.

From a solid cylinder whose height is 2.4 cm and diameter of 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm².

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