Question

A spherical canon ball, 28 cm in diameter is melted and cast into a right circular conical mould, the base of which is 35 cm in diameter.Find the height of cone, correct to one place of decimal.

Answer 1

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Secondary School Math 5 points

A spherical cannon ball 28cm in diameter is melted and recast in to a right conical mould base of which is 35 cm in diameter find the height of the cone

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Answers

ishu146

ishu146 Expert

Sphere radius = 28 /2 =14 cm

volume of sphere = 4/3 pie r^3

=4/3 pie ×14 ×14×14

it's melted and recast to a conical shape

it's radius =35 /2 =17.5 cm

=1/3 pie r^2 h

1/3 pie ×17.5 ×17.5 ×h

according to the question

volume of sphere =volume of cone

4/3 pie 14 ×14 ×14 =1/3 pie 17.5 ×17.5 ×h

4/3 ×14 ×14×14 =1/3 ×17.5 ×17.5 ×h

3658.6 =102.08 ×h

3658.6 /102.08 =h

35.84 =h ok keep samile ✌ follow me

Answer 2

☯ Let h cm be the height of the cone.

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We have,

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• Diameter of spherical canon ball = 28 cm
• Radius of base of the spherical canon ball = 28/2 = 14 cm
• Diameter of the base of the cone = 35 cm
• Radius of base of the cone = 35/2 cm

⠀⠀⠀

Now,

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★ Volume of cone = Volume of Spherical canon ball

⠀⠀⠀

$:\implies\sf \dfrac{1}{3} \times \pi \times \bigg\lgroup \dfrac{35}{2} \bigg\rgroup^2 \times h = \dfrac{4}{3} \times \pi \times (14)^2$

$\qquad\quad:\implies\sf \bigg\lgroup \dfrac{35}{2} \bigg\rgroup^2 h = 4 \times (14)^2$

$\quad:\implies\sf \bigg\lgroup 4 \times 14 \times 14 \times 14 \times \dfrac{2}{35} \times \dfrac{2}{35} \bigg\rgroup$

$\qquad:\implies\sf \bigg\lgroup 4 \times 2 \times 2 \times 14 \times \dfrac{2}{5} \times \dfrac{2}{5} \bigg\rgroup$

$\qquad\qquad\qquad\quad:\implies\sf \dfrac{896}{25}$

$\qquad\qquad\quad:\implies{\boxed{\frak{\pink{35.84\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Height\;of\;cone\;is\; \bf{35.84\;cm}.}}}$