Question

a trophy awarded to the best student in the class is in the form of a solid cylinder mounted on a solid hemisphere with the same radius and is made from some metal. this trophy is mounted on a wooden cuboids. the diameter of the hemisphere is 21cm and the total height of the trophy is 24.5cm. find the weight of metal of the used in making the trophy, if the weight of 1cm³ of the metal is 1.2g.(use π=227)

Answer 1

Total weight of trophy =  10.3 Kg

Given:

A trophy awarded to the best student in the class is in the form of a solid cylinder mounted on a solid hemisphere with the same radius and is made from some metal.

This trophy is mounted on a wooden cuboids. the diameter of the hemisphere is 21 cm. and the total height of the trophy is 24.5 cm.

To find:

The weight of metal of the used in making the trophy, if the weight of 1cm³ of the metal is 1.2 g.

Explanation:

Volume of hemisphere = $\frac{2}{3}$ × $\pi$ × $R^3$

Volume of cylinder = $\pi$ × r²× h

Where  R= radius of the hemisphere

Total height of the trophy = Height of cylinder + Radius of the hemisphere

                                 24.5 = Height of cylinder + 11.5

              Height of cylinder = 13 cm

Volume of hemisphere = $\frac{2}{3}$ × $\pi$ × $R^3$

Volume of hemisphere =  $\frac{2}{3}$ × $\pi$ × $11.5^3$

Volume of hemisphere = 3185.31 cm³

Given that radius of the hemisphere = radius of the cylinder

Volume of cylinder = $\pi$ × r²× h

Volume of cylinder = $\pi$ × 11.5²× 13

Volume of cylinder = 5401.18 cm³

Total volume of trophy = 3185.31 + 5401.18 = 8586.49 cm³

The weight of 1cm³ of the metal is 1.2 g.

Total weight of trophy = 8586.49 × 1.2 =10303.79 g = 10.3 Kg

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