Question

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

Answer 1

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Answer 2

Given:

Side of cubical block, a= 7 cm

To find:

Greatest diameter of hemisphere and surface area of solid.

Solution:

Greatest diameter of hemisphere=Side of cube

Diameter of hemisphere, d=7 cm

Radius of hemisphere, r=d/2=7/2 cm

We know that

Surface area of cube=$6a^2$

Surface area of hemisphere=$2\pi r^2$

Where$\pi=\frac{22}{7}$

Using the formula

Surface area of solid

=Surface area of cube+ surface area of hemisphere-area of circular base

=$6a^2+2\pi r^2-\pi r^2$

$6a^2+\pi r^2$

Substitute the values

Surface area of solid

=$6(7^2)+\frac{22}{7}\times (7/2)^2$

$=294+38.5 cm^2$

$=332.5cm^2$

Hence, surface area of solid$=332.5cm^2$