Mathematics

The cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.

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It’s known that, the diameter of the largest hemisphere that can be placed on the face of a cube of side 7 cm will be 7 cm.

So, it’s radius (r) = $\dfrac{7}{2}$ = 3.5 cm

Curved surface area = 2πr²

= $2 \times \dfrac{22}{7} \times (3.5)^2$ = 77 cm².

Area of base of hemisphere = πr²

= $\dfrac{22}{7} \times (3.5)^2$

= 38.5 cm².

From figure,

Surface area of the resulting solid = Surface area of the cube – Area of the base of the hemisphere + Curved surface area of hemisphere

= 6(side)² - 38.5 + 77

= 6(7)² + 38.5

= 294 + 38.5

= 332.5 cm².

Hence, surface area of resulting solid = 332.5 cm³.

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