Question

If h, c, v, are respectively the height, the curred
Surface and volume of a Cone prove that
3avh^3 = c²h ² + gv^2 = 0​

Answer 1

Given---> If h , c and v are respectively height , curved surface area and volume of cone .

To prove ---> 3 π v h³ - c² h² + 9 v² = 0

Proof---> We know that,

Curved surface area of cone = π r l

Volume of cone = 1 / 3 π r² h

and , l² = r² + h²

LHS = 3π v h³ - c² h² + 9 v²

= 3π ( 1/3 ) π r²h h³ - ( π r l )² h² + 9 ( 1/3 π r² h )²

= π² r² h⁴ - π² r² l² h² + 9 ( 1 / 9 π² r⁴ h² )

= π² r² h⁴ - π² r² h² ( l² ) + π² r⁴ h²

= π² r² h⁴ - π² r² h² ( r² + h² ) + π² r⁴ h²

= π² r² h⁴ - π² r² h² r² - π² r² h² h² + π² r⁴ h²

= π² r² h⁴ - π² r⁴ h² - π² r² h⁴ + π r⁴ h²

= 0 = RHS

Additional identities--->

1) Volume of cube = edge³

2) Lateral surface area of cube = 4 edge²

3) Total surface area of cube = 6 edge²

4) Volume of cuboid = l b h

5) Total surface area of cuboid

= 2 ( lb + bh + lh )

6) Lateral surface area of cuboid = 2 ( l + b ) h

#Answerwithquality

#BAL

Answer 2

Step-by-step explanation:

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