Question

A solid right circular cylinder of radius 60cm and height 20 cm is melted and recast into a right citcular cone of height 3 times that of the cylinder .find the curved surface area of cone

Answer 1

Answer:

Step-by-step explanation: volume of cylinder = volume of cone formed

22/7*60*60*20 = 1/3*22/7*r^2*60

226194.67 = 62.83*r^2

r^2= 3600.10

r= 60

csa of cone= 22/7* 60*84.85

csa of cone= 15993.84

Answer 2

The curved surface area of cone is $16000.81 cm^2$

Step-by-step explanation:

Radius of cylinder = 60 cm

Height of cylinder = 20 cm

Volume of cylinder =$\pi r^2 h = \frac{22}{7} \times 60^2 \times 20$

A solid right circular cylinder is melted and recast into a right circular cone of height 3 times that of the cylinder

Height of cone = 3 times of the cylinder = 3 (20)=60 cm

Volume of cone =$\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 60$

Volume of cylinder = volume of cone

$\frac{22}{7} \times 60^2 \times 20= \frac{1}{3} \times \frac{22}{7} \times r^2 \times 60$

$60 \times 20= \frac{1}{3} \times r^2$

$3 \times 60 \times 20=r^2$

$\sqrt{3 \times 60 \times 20}=r$

$60=r$

Radius of cone = 60 cm

Curved surface area of cone= $\pi r \sqrt{h^2+r^2} = \frac{22}{7} \times 60 \times \sqrt{60^2+60^2}=16000.81 cm^2$

Hence the curved surface area of cone is $16000.81 cm^2$

#Learn more :

A solid right circular cone of height 120cm and radius 60cm is placed in a right circular cylinder full of water of height 180cm such that it touches the bottom. Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of the cone.

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