NCERT Solutions for Class 9 Maths Chapter 13
Important NCERT Questions
Surface Areas and Volumes
NCERT Books for Session 2022-2023
CBSE Board, UP Board and Other state Boards
EXERCISE 13.7
Page No:233
Questions No:6
(i) height of the cone.
(ii) slant height of the cone.
(iii) curved surface area of the cone.
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(I) Volume of cone V = 9856 cm³ and radius r = 28/2 = 14 cm
Let, the height of cone be h cm, therefore volume of cone = 1/3πr²h
⇒ 9856 = 1/3 × 22/7 × 14 × 14 × h
⇒ 9856 = 1/3 × 22 × 2 × 14 × h
⇒ h = 9856 × 3/22 × 2 × 14 ⇒ h = 48 cm
Hence, the height of cone is 48 cm.
(II) Height of cone h = 48 cm and radius r = 14 cm
Let, the slant height of cone = l cm
We, know that, l² = h² + r²
⇒ l² = 48² + 14² ⇒ l² = 2304 + 196
⇒ l² = 2500 ⇒ l = √2500 = 50 cm
Hence, the slant height of cone is 50 cm.
(III) Slant height of cone l = 50 cm and radius r = 14 cm
Curved surface area of cone = πrl
= 22/7 × 14 × 50 = 22 × 2 × 50 = 2200 cm²
Hence, the curved surface area of cone is 2200 cm².