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741.
The volume of a hemisphere is 2425 $\frac{1}{2}$ cm³^. Find its curved surface area.
$[Use π = \frac{22}{7}]$

Given: Volume of a hemisphere = 2425 $\frac{1}{2}$ cm³ = $\frac{4851}{2}$ cm³.

Now, let r be the radius of the hemisphere

Volume of a hemisphere = $\frac{2}{3} {πr}^{3}$

$∴ \frac{2}{3} {πr}^{3} = \frac{4851}{2} \Rightarrow \frac{2}{3} x \frac{22}{7} x r^{3} = \frac{4851}{2} \Rightarrow r^{3} = \frac{4851}{2} x \frac{3}{2} x \frac{7}{22} = {(\frac{21}{2})}^{3} ∴ r = \frac{21}{2} cm$

So, curved surface area of the hemisphere = $2 {πr}^{2}$

= $2 x \frac{22^{11}}{7} x \frac{21^{3}}{2} x \frac{21}{2}$

= 693 sq. cm.

Long Answer Type

742.

From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. $[Use π = \frac{22}{7}]$

OR

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.

743.

A bucket is in the form of a frustum of a cone and its can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. $[use π = \frac{22}{7}]$

744.

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.

$[Use π = \frac{22}{7}]$