Question

The cost of painting the total surface area of a cone at 25 paise per cm square is rupees 176 find the volume of the cone if its slant height is 25 cm

Answer 1

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Answer 2

Answer:

The volume of the cone is 1232 cm.cube.

Step-by-step explanation:

Given : The cost of painting the total surface area of a cone at 25 paise per cm square is rupees 176.

To find : The volume of the cone if its slant height is 25 cm?

Solution :

Total cost = Rs. 176

Rate of charge = 25 paise per sq.cm = Rs. 0.25 per sq.cm 

Total cost of painting cone = Total surface area of cone × Rate of charge

=> Total surface area of cone = Total cost of painting cone / Rate of charge

$= \frac{176}{0.25}= 704cm^2$

Let radius of cone be r cm

Slant height (l) = 25 cm

Total surface area of cone is

$TSA=\pi r(r+l)$

$704=3.14 r(r+25)$

$224=r(r+25)$

$r^2+25r-224=0$

$r^2+32r-7r-224=0$

$r(r+32)-7(r+32)=0$

$(r-7)(r+32)=0$

$r=7,-32$

Reject negative value, r=7

Therefore, radius of cone = 7 cm

By Pythagoras Theorem, height of cone is

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

$h=\sqrt{25^2-7^2}$

$h=\sqrt{625-49}$

$h=\sqrt{576}$

$h=24$

Therefore, volume of cone is

$V=\frac{1}{3}\pi r^2h$

$V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24$

$V=1232cm^3$

Therefore, The volume of the cone is 1232 cm.cube.