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The Radius and Height of a Right Circular Cone Are in the Ratio 5 : 12 and Its Volume is 2512 Cubic Cm. Find the Slant Height and Radius of the Cone. (Use It 𝜋 = 3.14). - CBSE Class 9 - Mathematics

ConceptSurface Area of a Right Circular Cone

Question

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use it 𝜋 = 3.14).

Solution

Let the ratio be x

Radius ‘r’ = 5x
Height ‘h’ = 12x

∴ Slant height l =sqrt(r^2+h^2)=sqrt((5x)^2+(12x)^2)=13x

Now volume = 2512cm^3

⇒ 1/3xxpixx(5x)^2xx12x=2512

⇒ 1/3xx3.14xx25x^2xx12x=2512

⇒ x^3=(2512xx3)/(314xx25xx2)

⇒ x=2

∴ Slant height = 13x=13xx2=26cm

And, Radius of cone =5x=5xx2=10cm

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APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 20: Surface Areas and Volume of A Right Circular Cone
Ex.20.20 | Q: 5 | Page no. 21
Solution The Radius and Height of a Right Circular Cone Are in the Ratio 5 : 12 and Its Volume is 2512 Cubic Cm. Find the Slant Height and Radius of the Cone. (Use It 𝜋 = 3.14). Concept: Surface Area of a Right Circular Cone.
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