Question

Find the capacity in liters of a conical vessel with
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm

Answer 1

(i) Radius of the cone, r = 7cm
Slant height of the cone, l = 25cm
Height of the cone, \(h = \sqrt{l² - r²}\)
\(= \sqrt{(25)² - (7)²}\)
\(= \sqrt{625 - 49}\)
\(= \sqrt{576}\)
h = 24 cm

Volume of cone =\( \frac{1}{3}\) \(\pi \)r²h
= \(\frac{1}{3}\) × \(\frac{22}{7}\) × 7 cm × 7 cm × 24 cm
= 1232 cm³
= 1232 × (\(\frac{1}{1000}\)L) 
= 1.232 liters

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(ii) Height of the cone, h = 7cm
Slant height of the cone, l = 13cm
Radius of the cone, \(r = \sqrt{l² - h²}\)
\(= \sqrt{(13)² - (12)²}\)
\(= \sqrt{169 -144}\)
\(= \sqrt{25}\)
r = 5 cm

Volume of the cone = \(\frac{1}{3}\)\(\pi\)r²h
= \(\frac{1}{3}\) × \(\frac{22}{7}\) × 5 cm × 5 cm × 12 cm
\(= \frac{2200}{7}\) cm³
\(= \frac{2200}{7} × \frac{1}{1000}\ L \)
\(=\frac{ 11}{35}\) litres