Question

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find. 
(i) height of the cone 
(ii) slant height of the cone 
(iii) curved surface area of the cone

Answer 1

(i) Radius of cone =\(\frac{28}{2}\) cm = 14 cm 
Let the height of the cone be h.
Volume of cone = 9856 cm³

\(⇒\frac{1}{3}\pi\)r²h = 9856 cm³

h \(= \frac{9856\ cm^3 × 3}{\pi r²}\)

\(= \frac{9856\ cm^3 × 3}{(14\ cm × 14\ cm) }× \frac{7}{22}\)
= 48 cm
So, the height of the cone is 48 cm.

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(ii) Slant height of the cone, \(l = \sqrt{r² + h²}\)
\(= \sqrt{(14)² + (48)²}\)

\(= \sqrt{196 + 2304}\)

\(= \sqrt{2500}\)
= 50 cm
So, the slant height of the cone is 50 cm.

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(iii) Curved surface area of the cone= \(\pi\)rl
\(= \frac{22}{7}\)× 14 cm × 50 cm
= 2200 cm²
Therefore, the curved surface area of the cone is 2200 cm² .