The height and the radius of the cone is in the ratio of 4:3 if the volume is 96pi cm3 find the slant height of the cone
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Step-by-step explanation:
Given---> Height and radius of cone is in the ratio 4 : 3 and volume is 96 π cm³ .
To find---> height and radius of cone
Solution----> ATQ,
Ratio of height and radius is 4 : 3 .
Let height be 4x and radius be 3x .
Volume of cone = 96 π Cm³
=> 1 / 3 π r² h = 96 π
=> r² h = 96 × 3 × π / π
=> ( 3 x )² ( 4 x ) = 96 × 3
=> ( 9 x² ) ( 4 x ) = 96 × 3
=> 36 x³ = 96 × 3
=> x³ = 96 × 3 / 36
=> x³ = 8 × 3 / 3
=> x³ = 8
=> x³ = 2³
=> x = 2
Height of cone = 4x
= 4 ( 2 )
= 8 Cm
Radius of cone = 3x
= 3 ( 2 )
= 6 Cm
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