Question

The cost of painting the tsa of cone at 25 Paise per square cm is rs 176.find the volume of the cone if its slant height is 25 cm

Answer 1

SOLUTION:-

Given:

The cost of painting the Total surface area of cone at 25 paise cm² is Rs.176.

•Slant height of cone is 25cm.

To find:

The volume of the cone.

Explanation:

Formula of the T.S.A Of the cone.

=) πrl + πr²

We have,

25 paise in Rupees

=) 0.25 rupees.

$= > \frac{176}{0.25} \\ \\ = > \frac{176 \times 100}{0.25 \times 100} \\ \\ = > \frac{17600}{25} \\ \\ = > 704 {cm}^{2}$

So,

Formula: πr(r+l)

$= > \frac{22}{7} \times r(r + 25) = 704 \\ \\ = > {r}^{2} + 25r = 32 \times 7 \\ \\ = > {r}^{2} + 25r = 224 \\ \\ = > {r}^{2} + 25r - 224 = 0 \\ \\ = > {r}^{2} + 32r - 7r - 224 = 0 \\ \\ = > r(r + 32) - 7(r + 32) = 0 \\ \\ = > (r + 32)(r - 7) = 0 \\ \\ = > r + 32 = 0 \: \: or \: \: r - 7 = 0 \ \\ \\ \ = > r = - 32 \: \: \: or \: \: \: \: r = 7$

Negative value isn't acceptable.

So,

r= 7cm

Now,

Slant Height= √h² + r²

$= > l = \sqrt{ {h}^{2} + {r}^{2} } \\ \\ = > 25 = \sqrt{ {h}^{2} + {7}^{2} } \\ \\ = > {h}^{2} = {25}^{2} - {7}^{2} \\ \\ = > {h}^{2} = 625 - 49 \\ \\ = > {h}^{2} = 576 \\ \\ = > h = \sqrt{576} \\ \\ = > h = 24cm$

&

Volume of the cone:

$= > \frac{1}{3} \pi {r}^{2} h \\ \\ = > \frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 24 \\ \\ = > (22 \times 7 \times 8) {cm}^{3} \\ \\ = > 1232 {cm}^{3}$

Thus,

The volume of cone is 1232cm³.

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