Question

A cylindrical bucket, whose base has a radius of
15 cm, is filled with water up to a height of 20 cm. A
heavy iron spherical ball of a radius 10 cm is dropped
to submerge completely in water in the bucket. Find
the increase in the level of water.​

Answer 1

$\huge\sf\pink{Answer}$

☞ Your Answer is 14.08 cm

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$\huge\sf\blue{Given}$

✭ There is a cylinder of radius 15 cm and height 20 cm is filled with water

✭ A sphere of radius 10 cm is immersed inside the cylinder

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

◈ The water displaced?

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$\huge\sf\purple{Steps}$

$\sf \large\underline{\underline{\sf Concept}}$

So here simply find the volume of the cylinder and volume of the sphere seperately, the difference in their volume is the water that rices up

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Volume of a cylinder is given by,

$\sf \underline{\boxed{\sf Volume_{Cylinder} = \pi r^2h}}$

◕ Radius = 15 cm

◕ Height = 20 cm

Substituting the given values,

➝ $\sf Volume_{Cylinder} = \pi r^2h$

➝ $\sf Volume = \dfrac{22}{7} \times 15^2 \times 20$

➝ $\sf Volume = \dfrac{22}{7} \times 225 \times 20$

➝ $\sf Volume = \dfrac{22}{7} \times 4500$

➝ $\sf \green{Volume = 14142.86 \ cm^3}$

Volume of sphere is given by,

$\underline{\boxed{\sf Volume_{Sphere} = \dfrac{4}{3} \times \pi \times r^3}}$

◕ Radius = 10 cm

Substituting the given values,

➳ $\sf Volume_{Sphere} = \dfrac{4}{3} \times \pi \times r^3$

➳ $\sf Volume = \dfrac{4}{3} \times \dfrac{22}{7} \times 10^3$

➳ $\sf Volume = \dfrac{4}{3} \times \dfrac{22}{7} \times 1000$

➳ $\sf \green{Volume = 4190.48 \ cm^3}$

So now the water displaced will be,

»» $\sf Volume_{Cylinder} - Volume_{Sphere}$

»» $\sf 14142.86 - 4190.48$

»» $\sf\red{Water \ Displaced = 9952.38 \ cm^3}$

So how we shall find the height of the water displaced by assuming a cylinder with,

• Radius = 15 cm
• Volume = 9952.38
• Height = ?

Substituting the values in the formula for volume of a cylinder,

➢ $\sf Volume_{Cylinder} = \pi r^2h$

➢ $\sf 9952.38 = \dfrac{22}{7} \times 15^2 \times h$

➢ $\sf 9952.38 = \dfrac{22}{7} \times 225 \times h$

➢ $\sf 9952.38\times \dfrac{7}{22 \times 225} = h$

➢ $\sf\orange{Height = 14.08\ cm}$

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