Question

The curved surface area of a right circular cone 12320cm2. If the radius of the base is 56cm , find
the height of the cone.

Answer 1

Given :

• Right circular cone = 12320cm²
• Radius of the base = 56cm

To Find :

• Height of the cone

Solution :

We have, π = 22/7 and r = 56

So to find the height of the cone. First we have to find the curved surface area of a right circular cone.

By using formula,

⇒ CSA of cone = 12320

⇒ πrl = 12320

⇒ 22/7 × 56 × l = 12320

⇒ l = 12320 × 7 / 22 × 56

⇒ l = 86240 / 1232

⇒ l = 43120 / 616

⇒ l = 21560 / 308

⇒ l = 10780 / 154

⇒ l = 5390 / 77

⇒ l = 70cm

We have, l = 70cm and r = 56cm

Now we have to find height of the cone

By using Formula,

⇒ Height of the cone = √l² - r²

⇒ Height of the cone = √70² - 56²

⇒ Height of the cone = √4900 - 3136

⇒ Height of the cone = √1764

⇒ Height of the cone = 42cm

•°• Height of the cone = 42cm

__________________________

Answer 2

${\huge {\underline {\bf {\blue {Question}}}}}$

The curved surface area of a right circular cone is 12320 ${\sf {cm}^{2}}$ . If the radius of the base is 56cm, find the height of the cone.

${\huge {\underline {\bf {\blue {Answer}}}}}$

Given :-

• The curved surface area of a right circular cone is 12320 ${\sf {cm}^{2}}$
• The radius of the base is 56 cm

To Find :-

• Height of the cone.

Solution :-

Use $\pi$ = $\sf \dfrac {22}{7}$

$\implies$ Curved surface area of cone is 12320 ${\sf {cm}^{2}}$

${\boxed {\sf { Curved~ Surface~ area~ of~ cone = \pi r l }}}$

$\implies$ $\sf \pi r l$ = 12310 ${\sf {cm}^{2}}$

$\implies$ ${\sf {{\dfrac {22}{7}} \times 56 \times l = 12320}}$

$\implies$ ${\sf {{\dfrac {22}{{\cancel{7}}} \times {\cancel {{56}}^{8} \times l = 12320}}}}$

$\implies$ ${\sf {22 \times 8 \times l = 12320}}$

$\implies$ ${\sf {176 \times l = 12320}}$

$\implies$ ${\sf {l = {\dfrac {12320}{176}}}}$

$\implies$ ${\sf {l = {\dfrac {\cancel {12320}}{{\cancel{176}}}}}}$

$\implies$ ${\underline {\boxed {\sf {Slant~ height (l) = 70 cm}}}}$

Now, we have Slant height = 70 cm and radius = 56 cm.

${\boxed {\sf {Height~ of~ cone = {\sqrt {{length}^{2} - {radius}{2}}}}}}$

Substitute the value of length and radius in the above formula.

$\implies$ ${\sf {Height~ of~ cone = {\sqrt {{70}^{2} - {56}^{2}}}}}$

$\implies$ ${\sf {Height~ of~ cone = {\sqrt {4900 - 3136}}}}$

$\implies$ ${\sf {Height~ of~ cone = {\sqrt {1764}}}}$

$\implies$ ${\underline {\boxed {\sf {Height~ of~ cone = 42 cm}}}}$

${\sf {\underline {\purple {Hence,~ height~ of~ the~ cone~ is~ 42~ cm.}}}}$