Question

the area of the ring is 40πcm^3. if the width of the ring is 4cm, find the .
(¡) sum of the radio of the circle
(¡¡) the difference in the circumference of the circle .​

Answer 1

$\sf\large{\underline{\green{\underline{\red{Question:-}}}}}$

the area of the ring is 40πcm^3. if the width of the ring is 4cm, find the .

• (¡) sum of the radio of the circle
• (¡¡) the difference in the circumference of the circle .

$\sf\large{\underline{\pink{\underline{\red{Given:-}}}}}$

• $\sf area\: of \:the \:Ring = 40πcm^3$

• $\sf width\:of\:the\:ring= 4cm$

$\sf\large{\underline{\blue{\underline{\red{To\:Find:-}}}}}$

• sum of the radio of the circle .
• the difference in the circumference of the circle .

$\sf\large{\underline{\red{\underline{\green{FORMULA\:USED:-}}}}}$

$\sf{\fbox{\red{\underline{\blue{Area\:of\:ring= π(R^2-r^2)}}}}}$

$\sf\large{\underline{\green{\underline{\red{Solution:-}}}}}$

$\sf→ Area\:of\:ring= π(R^2-r^2)= 40π\\\sf→ (R+r)(R-r)=40\\\sf→ (R+r)=40\\\sf→ (R+r)=\frac{40}{4}\\\sf→ R+r=10cm$

$\rule{220}$

$\sf→ R+r=10 \\\sf→{\underline{R-r=4}}$

$\sf→ 2R=14\\\sf→ R=\frac{14}{2}\\\sf→ R=7\\\sf→ r=3cm$

Now,

Difference in the circumference of the circle

$\sf→ 2πR-2πr\\\sf→ 2π(R-1)$

$\sf→2π(4)=8πcm$

Answer 2

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