Maths-
General
Easy
Question
A cone has slanted height of 5cm and height of 4cm, its volume (in cm3 ) is
__________
- 38.71
- 36.50
- 37.00
- 37.68
Hint:
Volume of a cone = (1/3)πr2h
By applying Pythagoras theorem on the cone, we can find the relation between volume and slant height of the cone.
We know, h2 + r2 = L2
![h equals square root of open parentheses L squared minus r squared close parentheses end root](data:image/png;base64,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)
where,
h is the height of the cone,
r is the radius of the base, and,
L is the slant height of the cone.
The volume of the cone in terms of slant height can be given as
V = (1/3)πr2h = ![left parenthesis fraction numerator begin display style 1 end style over denominator 3 end fraction right parenthesis pi r squared square root of open parentheses L squared minus r squared close parentheses end root](data:image/png;base64,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)
The correct answer is: 37.68
We have given that
Slanted height L = 5 cm
Height, h = 4cm
From these given values we can find the radius of base of cone
We know that
h2 + r2 = L2
r2 = L2 - h2
= 52 – 42
= 25 – 16
r2 = 9
r= 3
So, the volume of cone = (
)πr2h
= (
)(3.14)(3 x 3)(4)
= 3.14 x 3 x 4
= 37.68
Therefore, the correct option is d) 37.6
So, the volume of cone = (
Therefore, the correct option is d) 37.6
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