Question

A solid right circular cylinder is made by melting a solid right circular cone. The radii of both are equal. If the height of the cone is 15cm., then let us determine the height of the solid cylinder.
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Answer 1

Given :

• A solid cylinder is made by melting a solid right circular cone.
• The radii of both are equal.
• Height of the cone is 15 cm.

To find :

• Height of the solid cylinder.

Solution :

Consider ,

• Radii of cylinder = Radii of cone = r cm.
• Height of cylinder = h cm

Formula Used :

★${\boxed{\sf{Volume\:of\: cylinder=\pi\:r^2h}}}$

★${\boxed{\sf{Volume\:of\:cone=\dfrac{1}{3}\pi\:r^2\:h}}}$

Volume of cylinder = πr²h cm³

• Height of cone = 15 cm

Volume of cone = $\sf{\dfrac{1}{3}\pi\:r^2\times\:15\:cm^3}$

→ Volume of cone = 5πr² cm³

According to the question ,

$\sf{Volume\:of\: cylinder=Volume\:of\:cone}$

$\to\sf{\pi\:r^2\:h=5\pi\:r^2}$

$\to\sf{h=5}$

Therefore, height of the solid cylinder is 5 cm.

Answer 2

Question:

A solid right circular cylinder is made by melting a solid right circular cone. The radii of both are equal. If the height of the cone is 15cm , then let us determine the height of the solid cylinder.

To find:

To find the height of the cylinder.

Answer:

$\underline{ \: \underline{ \: \bold{\sf \pink{H = 5cm}} \: } \: }$

Height of the cone is 5cm .

Given:

Height of the cylinder ( H ) = ?

Height of the cone ( h ) = 15cm

Radius of the cylinder ( r ) = r cm

Radius of the cone ( r ) = r cm

Step-by-step explanation:

We know that, volumes are equal.

$\boxed{Volume \: of \: the \: cylinder=Volume \: of \: the \: cone}$

$\implies \not{\pi} \not{ {r}^{2}}H = \frac{1}{3} \not{\pi} \not{ {r}^{2}}h$

$\implies H = \frac{1}{3} \times 15$

$\implies\boxed{H = 5cm}$

$\therefore Height \: of \: the \: cone \: is \: 5cm$

Formula used:

$\star Volume \: of \: the \: cylinder = \pi {r}^{2} h$

$\star Volume \: of \: the \: cone = \frac{1}{3} \pi {r}^{2} h$