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  • From a solid cylinder whose height is 2.4 cm and diameter 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 cm 2 .

8. From a solid cylinder whose height is 2.4 cm and diameter 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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Firstly, we need to calculate the slant height of cone :

                                                      l^2\ =\ r^2\ +\ h^2

or                                                         =\ (0.7)^2\ +\ (2.4)^2

or                                                    l^2\ =\ 6.25

or                                                   l\ =\ 2.5\ cm

Now, the total surface area of solid can be calculated as follows:

The surface area of solid = Surface area of cylinder + Surface area of cone + Area of base of the cylinder

 The surface area of the cylinder is =\ 2 \pi rh

or                                          =\ 2 \pi \times 0.7\times 2.4

or                                         =\ 10.56\ cm^2

Now, the surface area of a cone  =\ \pi rl

or                                         =\ \pi \times 0.7\times 2.5

or                                         =\ 5.50\ cm^2

And the area of the base of the cylinder is   =\ \pi r^2

or                                                      =\ \pi \times 0.7\times 0.7

or                                                      =\ 1.54\ cm^2

Thus, the required area of solids is: 10.56 + 5.50 + 1.54 = 17.60 cm2.

Thus, the total surface area of the remaining solid to the nearest cm2 is 18 cm2.

Posted by

Devendra Khairwa

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