Question

The cost of painting the total surface area of a cone at 25paise per cm² is Rs 176 .Find the volume of cone ,if it's slant height is 25 cm

Answer 1

Given total cost =Rs.176

Rate of charge = 25 paise per sq.cm

The total cost of painting cone = Total surface area of cone × Rate of charge

⇒ Total surface area of cone =

Total cost of painting cone/rate of charge

= 176/0.25=704cm²

Let the radius of cone be rcm

slant height (l)=25cm

Total surface area of cone =πr(l+r)=704

⇒ 22/7×r(r+25)=704

⇒r² +25r= 704×7/ 24

⇒r²+25r=224

⇒r² +32r−7r−224=0

⇒r(r+32)−7(r+32)=0

⇒(r+32)(r−7)=0

Then r=7 and r=−32

Discarding negative value as radius cannot be negative

Therefore, radius of cone=7cm

By Pythagoras Theorem,

height of cone = l 2 −r 2

= (25) 2 −(7) 2

= 625−79

= 576=24 cm

Therefore, volume of cone = 1/3πr²h

= 1/3 ×22/7 × (7)² × 24

= 22×7×8

=1232cm³