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Find the capacity in liters of a conical vessel with

(i) radius 7 cm, slant height 25 cm. and
(ii) height 12 cm, slant height 13 cm.

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1.200 litres

and

\frac{11}{31} litres

122.5 litres

and

\frac{11}{33} litres

1.232 litres

and

\frac{11}{35} litres

12.35 litres

and

\frac{11}{38} litres

answer is C.

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Detailed Solution

Given,
The conical vessel's radius (r) =7 cm
Slant height (l) = 25 cm
Since, Vertical height

(h) = \sqrt{l^{2} - r^{2}}

\Rightarrow \sqrt{25^{2} - 7^{2}}

= \sqrt{625 - 49}

= \sqrt{576}

= 24 cm

So, Volume

(V) = \frac{1}{3} π r^{2} h

= \frac{1}{3} \times \frac{22}{7} \times 7 \times 24 {cm}^{3}

\Rightarrow 154 \times 8

= 1232 {cm}^{3}

Capacity in liter,

= \frac{1232 \times 1}{1000}

(1000

c m^{3}

=1 liter)

= 1.232 litres

(ii) Height

(h) = 12 cm

Slant height

(l) = 13 cm

∴ Radius = \sqrt{l^{2} - r^{2}} = \sqrt{(13)^{2} - (12)^{2}} = \sqrt{169 - 144} = \sqrt{25} = 5 cm

Now, volume we can calculate as,

V = \frac{1}{3} π r^{2} h = \frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times 12 {cm}^{3} = \frac{2200}{7} {cm}^{3} = 314.28 {cm}^{3}

Now, capacity in liters

= \frac{2200}{7 \times 1000} = \frac{22}{70}

= \frac{22}{70} = 0.314 litres

Option 3 is correct.

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