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 .