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Curved surface area of a cone is 308 cm^2 and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone. - CBSE Class 9 - Mathematics

ConceptSurface Area of a Right Circular Cone

Question

Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find

(i) radius of the base and (ii) total surface area of the cone.

["Assume "pi=22/7]

Solution

(i) Slant height (l) of cone = 14 cm

Let the radius of the circular end of the cone be r.

We know, CSA of cone = πrl

(308)cm^2=(22/7xxr xx14)cm

rArr r=(308/44)cm=7cm

Therefore, the radius of the circular end of the cone is 7 cm.

(ii) Total surface area of cone = CSA of cone + Area of base

= πrl + πr2

=[308+22/7xx(7)^2]cm^2

= (308 + 154) cm2

= 462 cm2

Therefore, the total surface area of the cone is 462 cm2.

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APPEARS IN

NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 13: Surface Area and Volumes
Ex. 13.30 | Q: 3 | Page no. 221

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Solution Curved surface area of a cone is 308 cm^2 and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone. Concept: Surface Area of a Right Circular Cone.
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