A cone height 8 m has a curved surface area 188.4 square meters find its volume.(take π=3.14).
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Given, height of the cone h = 8
Let r is the radius and l is the slant height of the cone.
Given curved surface area of the cone = 188.4
=> πrl = 188.4
=> πr√(r2 + h2 ) = 188.4 {since slant height l = √(r2 + h2 )}
=> 3.14*r√(r2 + 82 ) = 188.4
=> r√(r2 + 64 ) = 188.4/3.14
=> r√(r2 + 64 ) = 60
=> r2 *(r2 + 64 ) = (60)2
=> r4 + 64r2 = 3600
=> r4 + 64r2 - 3600 = 0
=> (r2 - 36)*(r2 + 100) = 0
=> r2 = 36, -100
Since square of a number can not be negative.
Hense, r2 = -100 is not possible
So, r2 = 36
=> r = ±6
Again since radius can not be negative.
So, r = 6
Now volume of the cone = (1/3)*πr2 h
= (1/3)*π*62h
= (3.41*36*8)/3
= 3.41*12*8
= 301.44 cm3
Let r is the radius and l is the slant height of the cone.
Given curved surface area of the cone = 188.4
=> πrl = 188.4
=> πr√(r2 + h2 ) = 188.4 {since slant height l = √(r2 + h2 )}
=> 3.14*r√(r2 + 82 ) = 188.4
=> r√(r2 + 64 ) = 188.4/3.14
=> r√(r2 + 64 ) = 60
=> r2 *(r2 + 64 ) = (60)2
=> r4 + 64r2 = 3600
=> r4 + 64r2 - 3600 = 0
=> (r2 - 36)*(r2 + 100) = 0
=> r2 = 36, -100
Since square of a number can not be negative.
Hense, r2 = -100 is not possible
So, r2 = 36
=> r = ±6
Again since radius can not be negative.
So, r = 6
Now volume of the cone = (1/3)*πr2 h
= (1/3)*π*62h
= (3.41*36*8)/3
= 3.41*12*8
= 301.44 cm3
Answered by
0
Given :-
- If a cone of height 8 M has a curved surface area of 188.4 m²
To Find :-
- Radius
- Volume
Solution :-
We know that
l² = r² + h²
l² = r² + (8)²
l² = r² + 64
l = √(r² + 64)
Now,
188.4 = 3.14 × r × √(r² + 64)
188.4/3.14 = r × √(r² + 64)
60 = r × √(r² + 64)
Squaring both side
(60)² = [r × √(r² + 64)]²
3600 = r²(r² + 64)
3600 = r⁴ + 64r²
0 = r⁴ + 64r² - 3600
0 = r⁴ + (100r² - 36r²) - 3600
0 = r⁴ + 100r - 36r² - 3600
0 = (r² + 100)(r² - 36)
Either
r² = -100
or
r² = 36
As length can't be negative
r² = 36
r = √36
r = 6
Now
Volume of cone = 1/3 × π × r² × h
Volume = 1/3 × 22/7 × (6)² × 8
Volume = 22/21 × 36 × 8
Volume = 22/7 × 12 × 8
Volume = 2112/7
Volume = 301.7 m³
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