The radhus and height of a solid right circular cone are in the ratio of 5:12.if its volume is 314cm cube 'find its t.s.a
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Ratio of radius : height of the cone = 5 : 12
So let the radius be 5x and height 12 x
The volume of cone= 1/3 * pi * r² * h
314= 1/3 * 3.14 * (5x)² * 12x (Volume of cone= 314 given)
314= 1/3 * 3.14 * 25x² * 12x
x³ = (314 *3 ) / 3.14 * 25 * 12
x³= 942/ 942
x³ = 1
x= 1
So radius= 5 cm and height = 12 cm
Slant height
⇒ l= √( h² - r²)
=√ ( 144 - 25)
=√ 169
= 13
So. TSA of cone= pi r ( r+ l)
=3.14 * 5 ( 5 + 13)
=15.7 * 18
=282.6 cm²
So let the radius be 5x and height 12 x
The volume of cone= 1/3 * pi * r² * h
314= 1/3 * 3.14 * (5x)² * 12x (Volume of cone= 314 given)
314= 1/3 * 3.14 * 25x² * 12x
x³ = (314 *3 ) / 3.14 * 25 * 12
x³= 942/ 942
x³ = 1
x= 1
So radius= 5 cm and height = 12 cm
Slant height
⇒ l= √( h² - r²)
=√ ( 144 - 25)
=√ 169
= 13
So. TSA of cone= pi r ( r+ l)
=3.14 * 5 ( 5 + 13)
=15.7 * 18
=282.6 cm²
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