Question

A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.​

Answer 1

Answer:

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Answer 2

Greatest diameter of hemisphere = side of cube = 7cm.

hence , base of hemisphere falls on cube , so that area should not from part of solid .

⠀⠀ Surface area of solid = Area of cube

Area of cube

Side = 7 cm

Area = 6a${^{2}}$

⠀ ⠀⠀= 6x(7x7)

⠀⠀⠀ = 6x49 = 294cm${^{2}}$

Curved surface area of hemisphere

diameter of hemisphere = 7cm

hence , radius of hemisphere =$\frac{7}{2}$

Curved surface area of hemisphere = 2πr${^{2}}$

⠀⠀⠀⠀ ⠀⠀= 2x$\frac{22}{7}$x$\frac{7}{2}$x$\frac{7}{2}$

⠀⠀⠀⠀ ⠀⠀= 77cm${^{2}}$

Base area of hemisphere

Base area of hemisphere is a circle with radius = radius of hemisphere = $\frac{7}{2}$

Base area of hemisphere = πr${^{2}}$

⠀⠀⠀⠀ ⠀⠀ = $\frac{22}{7}$x$\frac{7}{2}$x$\frac{7}{2}$

⠀⠀⠀⠀ ⠀⠀= $\frac{77}{2}$cm${^{2}}$

Surface area of solid = Area of cube

⠀⠀⠀+curved surface area of hemisphere

⠀⠀⠀⠀ ⠀⠀⠀⠀-Base area of hemisphere

= 294+77-$\frac{77}{2}$

= 332.5cm${^{2}}$

Surface area of solid = 332.5cm${^{2}}$

$\huge\orange{Hope~it~helps}$