Question

radius and slant height of cone are in ratio 7:25 .if its curved surface is 26950 sq.cm ,find its vertical height

Answer 1

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Answer 2

Answer:

The vertical height of the cone is 168 units .

Step-by-step explanation:

Formula

$Curved\ surface\ area\ of\ a\ cone = \pi r l$

Where r is the radius and l is the slant height .

As given

Radius and slant height of cone are in ratio 7:25 .

Let us assume that  be the scalar multiple of the radius and the slant height .

Thus

Radius = 7x

Slant Height = 25x

If its curved surface is 26950 sq.cm .

$\pi = 3.14$

Put all the values in the formula

$26950=3.14\times 7x\times 25x$

$26950=549.5x^{2}$

$x^{2} = \frac{26950}{550}$

$x^{2} = 49$

x = √49

x = 7 unit

Thus

Radius = 7x

           = 7 × 7

           = 49 units

Slant Height = 25x

           = 25 × 7

           = 175 units

Thus

l² = h² + r²

Put all the values in the above

175² = 49² + Height²

30625 - 2401 = Height²

28224 = Height²

Height = √28224

Height = 168 units

Therefore the vertical height of the cone is 168 units .