A wax Candle is in the shape of right circular cone with base radius 5 cm and height 12cm. It takes 1 hour 40 minutes to burn completely. After 25/2 minutes of burning the candle is reduced to a frustum with the height of h cm. Find the volume of the candle before burning, the total surface area of the candle before burning and the value of h.
Answers
2200/7 cm³ & 1980/7 cm² are Volume & TSA of candle before burning & h = 6 cm
Step-by-step explanation:
A wax Candle is in the shape of right circular cone with base radius 5 cm and height 12cm
=> Volume of Candle = (1/3)πr²h
= (1/3)(22/7)5² * 12
= 2200/7 cm³
Volume of candle before burning = 2200/7 cm³
Slant height = √5² + 12² = 13 cm
TSA = πr(r + l) = (22/7) * 5 ( 5 + 13) = 1980/7 cm²
It takes 1 hour 40 minutes to burn completely
=> 100 minutes to burn = 2200/7 cm³
=> 1 minute to burn = 22/7 cm³
=> 25/2 minutes to burn = 25 * 11 / 7 cm³
Volume burned of cone with height = 12 - h cm
and radius r
=> (12 - h)/r = 12/5
=> 12r = 5(12 - h)
=> r = 5(12 - h)/12
(1/3)(22/7)((5(12 - h)/12)²(12 - h) = 25 * 11 / 7
=> 22(12 - h)³ = 3 * 25 * 11 * 12² / (5²)
=> 22(12 - h)³ = 33 * 12²
=> 2(12 - h)³ = 3 * 12²
=> (12 - h)³ = 216
=> (12 - h)³ = 6³
=> 12 - h = 6
=> h = 6
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