Question

The radii of the circles ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm3, then find the value of r. [Use π =22 7]

Answer 1

$\huge\sf\pink{Answer}$

☞ r = 7cm

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$\huge\sf\blue{Given}$

✭ Volume of bucket = 5390 cm³

✭ Height = 15 cm

✭ R = 14 cm

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$\huge\sf\gray{To \:Find}$

☆ The value of r?

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$\huge\sf\purple{Steps}$

We know that the volume of the bucket is,

$\underline{\boxed{\green{\sf\dfrac{1}{3} \pi h (R^2 + r^2 + Rr)}}}$

Substituting the given values,

➝ $\sf 5390 = \dfrac{1}{3} × \dfrac{22}{7} × 15 ( 14^2 + r^2 + 14r)$

➝ $\sf 5390 = \dfrac{22}{7} × 5 ( 196 + r^2 + 14r)$

➝ $\sf 5390 × \dfrac{7}{110} = 196 + r^2 + 14r$

➝ $\sf 49×7 = 196 + r^2 + 14r$

➝ $\sf 343 = 196 + r^2 + 14r$

➝ $\sf 196 - 343 + r^2 + 14r = 0$

➝ $\sf r^2 + 14r - 147 = 0$

➝ $\sf r^2 + 21r - 7r - 147 = 0$

➝ $\sf r(r+21) - 7(r+21) = 0$

➝ $\sf (r-7)(r+21)$

So,

$\sf\red{\dashrightarrow r = 7 \ or \ r = (-21)}$

But we know that radius can't be negative so,

$\sf\orange{\dashrightarrow r = 7 \ cm}$

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Answer 2

Answer:

hope this helps u mate....