Question

13) The diameter of the base of metallic cone is
2 cm and height is 10 cm. 900 such cones are
melted to form 1 right circular cylinder whose
radius is 10 cm. Find height of the right circular
cylinder so formed.​

Answer 1

Answer:

H=30cm

Step-by-step explanation:

Radii of cone=1cm

Height of cone=10cm

Volume=1/3πr²h

1/3*π1*10*900

Vol of cylinder=πr²h

1/3*π1*10*900=π*100*h

h=3000π/100π

h=30cm.

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Answer 2

❥${\red{\underline{\underline{\large{\mathtt{Question:-}}}}}}$

The diameter of the base of metallic cone is 2 cm and height is 10 cm. 900 such cones are melted to form 1 right circular cylinder whose radius is 10 cm. Find height of the right circular cylinder so formed.

❥${\red{\underline{\underline{\large{\mathtt{Solution:-}}}}}}$

• Diameter of the base of cone=2cm.

• Height of cone= 10 cm.

We know that,

${\green{\boxed{\bold{Radius=\frac{Diameter}{2}}}}}$

So,the radius of cone=2/2= 1cm

${\blue{\boxed{\bold{Volume\:of\:cone=\frac{1}{3}πr^2h}}}}$

So, Volume of cone=$\frac{1}{3}π(1)^210$ cm³

$\:\:\:\:\:\:\:\:\:\:=\dfrac{1}{3}\pi10$ cm³

The volume of a cone = $\frac{1}{3}π10$ cm³

The volume of 900 cones = $\frac{1}{3}π10×900$ cm³

=3000π cm³

★900 cones are melted to form 1 right circular cylinder whose radius is 10 cm.

So, Volume of 900 cones= Volume of 1cylinder.

Radius of cylinder= 10 cm.

• Let the height of the right circular cylinder be = h cm.

${\orange{\boxed{\bold{Volume\:of\: cylinder=πr^2h}}}}$

So,

Volume of cylinder=π(10)²h cm³

= 100πh cm³

★ According to the question,

100πh = 3000π

→ 100h = 3000

→ h = 30

❥${\red{\underline{\underline{\large{\mathtt{Answer:-}}}}}}$

The height of the right circular cylinder is 30 cm.