Question

The volume,v,of a cone of height h and base radius r is 1/3 πr²h. A.obtain a formula for r.,B,find the base radius of a cone of height 14 cm and volume 91 2/3 cm³.(use the value 22/7 for π

Answer 1

r = 2.5 cm

Explanation:

Volume of cone:

a) To obtain the formula for r, isolate the term r² and then take square root to find 'r'.

`\sf Volume \ of \ cone \ V = (1)/(3)\pi r^2h`

`\sf (1)/(3)\pi r^2h = V\\\\\\ (1)/(3)*(22)/(7)*r^2*h= V\\\\`

`\sf r^2 = (V*3*7)/(h*22)\\\\Take \ square \ root \ both \sides,\\\\r = \sqrt{(V*3*7)/(h*22)}`

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b) h = 14 cm

`\sf V= 91 (2)/(3) \ cm^3\\~~~ =(275)/(3) \ cm^3`

`\sf r = \sqrt{(V*3*7)/(h*22)}\\\\~~ = \sqrt{((275)/(3)*3*7)/(14*22)}\\\\\\~~=\sqrt{(275*3*7)/(3*14*22)}\\\\~~=\sqrt{(25)/(2*2)}\\\\\\r = \sqrt{(5*5)/(2*2)}\\\\r = (5)/(2)\\\\\\\boxed{\bf r = 2.5 \ cm}`