Question

The slant height of a conical mountain is 2.5km and the are of this is 1.54km2 .find the height of the mountain

Answer 1

$\underline{ \underline{ \bold{Given : }}}$

• The slant height of a conical mountain = 2.5km

• The area of conical mountain = 1.54km²

$\underline{ \underline{ \bold{To \: find \: out : }}}$

Find the height of the conical mountain?

$\underline{ \underline{ \bold{Formula \: used : }}}$

$\boxed { \sf{Area \: of \: cone = \pi \: r \: l}}$

$\underline{ \underline{ \bold{Solution : }}}$

We know that,

Area of cone = πrl

⇒ 1.54 = 22/7 × r × 2.5

⇒ 1.54 = 55/7 × r

⇒ r = 1.54 × 7 / 55

⇒ r = 10.78 / 55

⇒ r = 0.196 km

Now,

By pythagoras therome

$\sf{ {l}^{2} = {r}^{2} + {h}^{2} }$

$\implies \sf{ {2.5}^{2} = {0.196}^{2} + {h}^{2} }$

$\implies \sf{ 6.25 =0.038416 + {h}^{2} }$

$\implies \sf{ {h}^{2} = 6.25 - 0.038416}$

$\implies \sf{ {h}^{2} = 6.21 \: \: (approx)}$

$\implies \sf{h = 2.49 \: \: (approx)}$

Hence, the height of the mountain is 2.49 km.

Answer 2

✰ Height = 2.49 km (approx) ✰

GIVEN:

• The slant height of a conical mountain is 2.5km
• C.S.A. of mountain is 1.54km²

TO FIND:

• What is the height of the mountain ?

FORMULA TO BE USED:

$\rm{ \star\: C.S.A. \: of \: cone = πrl \: \star }$

$\rm{ \star\: Slant \:height \: of \: cone = l^2 = h^2 + r^2 \: \star }$

SOLUTION:

Apply the formula of C.S.A. of the cone, and put the values in the formula

Take π = 22/7

$\mapsto$ 1.54 = 22/7 $\times$ r $\times$ 2.5

$\mapsto$ 1.54 $\times$ 7 = 22 $\times$ r $\times$ 2.5

$\mapsto$ 10.78 = r $\times$ 55

$\mapsto$ 10.78/55 = r

$\mapsto$ 0.196 km = r

Now, we have to find the height of the mountain

✒On putting the values in the formula, we get

$\mapsto$ l² = h² + r²

$\mapsto$ = (2.5)² = h² + (0.196)²

$\mapsto$ (2.5)² – (0.196)² = h²

$\mapsto$ 6.25 – 0.038416 = h²

$\mapsto$ 6.21 = h²

$\mapsto$ √6.21 = h

$\mapsto$ 2.49 km = h

❛ Hence, the height of the mountain is 2.49 km (approx) ❜