find the capacity in litres of a conical vessel with (I) radius 7cm, slant height 25cm. (ii) radius 12cm, slant height 13cm.
Answers
Answer:
Capacity of a conical vessel is nothing but the volume of the cone.
Volume of a cone of base radius r, and height h = 1/3πr2h
Slant height of the cone, l = √r² + h²
i) Radius of the conical vessel, r = 7cm
Slant height of the conical vessel, l = 25cm
Height of the conical vessel, h = √l² - r²
= √(25)² - (7)²
= √625 - 49
= √576
h = 24 cm
Capacity of the conical vessel = 1/3 πr²h
= 1/3 × 22/7 × 7 cm × 7 cm × 24 cm
= 1232 cm³
= 1232 × (1/1000L) [∵ 1000 cm³ = 1litre]
= 1.232 litres
ii) Height of the conical vessel, h = 7cm
Slant height of the conical vessel, l = 13cm
Radius of the conical vessel, r = √l² - h²
= √(13)² - (12)²
= √169 -144
= √25
r = 5 cm
Capacity of the conical vessel = 1/3πr²h
= 1/3 × 22/7 × 5 cm × 5 cm × 12 cm
= 2200/7 cm³
= 2200/7 × 1/1000 l [∵ 1000 cm³ = 1litre]
= 11/35 litres
Step-by-step explanation:
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Step-by-step explanation:
From Pythagoras theorem,
r2+h2=hs2
72+h2=252
⇒h2=576
⇒h=24cm
⇒ Volume=31πr2h
=31π×72×24
=2392πcm3=2000392πl
=1000190πl.
(ii) r2+h2=hs2 [Ref. image 2]
⇒122+r2=132
⇒r2=25
⇒r=5
⇒ Volume=31πr2h
=31π
hope you understand