Question

Asphere of diameter 6cm is moulded into a thin wire of diameter 0.22mm.Calculate the length of the wire in metres.Take22/7

Answer 1

Answer:

• 29.7736 m ≈ 30 m

Steps:

Concept:

• Volume of the original Sphere = Volume of the thin wire created

Given that,

Radius of sphere = 3 cm ( Diameter = 6 cm )

Hence finding the Volume of the sphere we get:

$\boxed{Volume = \dfrac{4}{3} \pi r^3}\\\\\\\implies Volume = \dfrac{4}{3} \times \dfrac{22}{7}\times (3)^3 \\\\\implies \text{Volume of the sphere} = \boxed{113.14\: cm^3}$

Also, it is given that the Diameter of the wire is 0.22 mm.

Hence the radius of the wire is = 0.11 mm = 0.011 cm

Calculating the Volume of the wire we get:

$\boxed{\text{Volume of Cylinder} = \pi r^2h}\\\\\\\implies Volume = \dfrac{22}{7} \times (0.11)^2 \times h\\\\\\\implies \boxed{Volume = 0.038\times h}$

Equating Both the volumes we get:

⇒ 113.14 = 0.038 × h

⇒ h = 113.14 / 0.038

⇒ h = 2977.36 cm = 29.7736 m ≈ 30 m

Hence the length of the wire is approximately 30 m long.

Answer 2

$\huge\red{\bf{\underline{\underline{Question:-}}}}$

A sphere of diameter 6cm is moulded into a thin wire of diameter 0.22mm.Calculate the length of the wire in metres. (Take $\pi = \frac{22}{7}$)

$\huge\red{\bf{\underline{\underline{Answer:-}}}}$

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$\red{\mathbb{\underline{GIVEN}}}$

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▪︎Diameter of sphere = 6cm

▪︎Diameter of wire = 0.22 mm

▪︎Volume of sphere = Volume of wire

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$\red{\mathbb{\underline{TO\ FIND}}}$

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▪︎Height of wire

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$\red{\mathbb{\underline{SOLUTION}}}$

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Radius of sphere = Diameter ÷ 2

= 6 ÷ 2

= 3cm

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Radius of wire = Diameter ÷ 2

= 0.22 ÷ 2

= 0.11mm

= 0.011cm

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According to given conditions;

A sphere is melted into wire

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So,

Volume of sphere = Volume of wire

= $\frac{4}{3}\pi {r}^{3}$ = $\pi {r}^{2}h$

= $\frac{4}{3}\pi {3}^{3}$ = $\pi× {0.011}^{2}×h$

= $\frac{4}{\cancel{3}}×\frac{22}{7}× 3 ×3 ×\cancel3$ = $\frac{22}{7}× 0.000121× h$

= 113.14 cm³ = 0.038 × h

= h = 113.14 ÷ 0.038

= h = 29.7736 cm

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$\boxed{Hence,\ Height\ =\ 30\ cm\ ( Approx.)}$

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$\red{\bf{\underline{\underline{Formulato be remembered:-}}}}$

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▪︎Volume of sphere = $\frac{4}{3}\pi {r}^{3}$

▪︎Volume of wire(cylinder) = $\pi {r}^{2}h$

▪︎Volume of cuboid = l × b × h

▪︎Volume of cube = (Side)³