Math, asked by SacredPsycho, 11 months ago

#Please help me with this question guyz!

→ If h, c, V are respectively the height, the curved surface and the volume of a cone, then prove that :

3πVh³ - C²h² + 9V² = 0

Answers

Answered by Anonymous

$<body bgcolor="pink">$

The curved surface area of a cone

=πrl

=πr√(h²+r²)

where h, l and r are the height, slant height and radius of the cone.

Volume of the cone

=πr²h/3

∴3πVh³-C²h²+9V²

=3π{(πr²h)/3}h³-{πr√(h²+r²)}²h²+9(πr²h/3)²

=π²r²h⁴-π²r²(h²+r²)h²+9π²r⁴h²/9

=π²r²h⁴-π²r²h⁴-π²r⁴h²+π²r⁴h²

=0 (Proved)

Answered by Anonymous

$\huge\mathfrak\pink{Bonjour!!}$

$\huge\mathcal\purple{Solution:-}$

⏩Let r and l denote respectively the radius of the base and slant height of the cone. Then,

l= √r² + h², V = 1/3 πr²h and C = πrl.

Therefore,

3πVh³ - C²h² + 9V²

= 3π × 1/3 πr²h × h³ - (πrl)²h² + 9 × [1/3 πr²h]²

= π²r²h⁴ - π²r²l²h² + π²r⁴h²

= π²r²h⁴ - π²r²h² (r² + h²) + π²r⁴h²

[Since, l² = r² + h²]

= π²r²h⁴ - π²r⁴h² - π²r²h⁴ + π²r⁴h² = 0.

[Hence Proved ⛄]

✔✔✔✔✔✔✔✔

⭐❤✨♥⭐❤✨♥⭐

Be Brainly...✌✌✌

♣ WALKER ♠

Previous Question

Next Question