Question

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

A) 54 cm B) 9 cm C) 27 cm D) 13.5 cm

Answer 1

We know:

$\Rightarrow volume\:of\:cylinder$

$\red{\boxed{πr^{2}h}}$

$\Rightarrow Volume\:of\:cone$

$\red{\boxed{πr^{2}\dfrac{h}{3}}}$

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Question:

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

Given:

$\text{Radius of the cylinder = 7cm }$

$\text{Height of the cylinder = 9cm}$

Concept:

• As the cone is melted from the the same cylinder the volume of the cylinder will be equal to the volume of cone..ie

$\red{\boxed{πr^{2}h = πr^{2}\dfrac{h}{3}}}$

• Given the radius is same in both the solids

Calculation:

$\blue{\boxed{7^{2} × 9 = 7^{2}\dfrac{h}{3}}}$

$\blue{\boxed{9 = \dfrac{h}{3}}}$

$\blue{\boxed{9 × 3 = h}}$

$\blue{\boxed{27 = h}}$

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$\text{Hence , the height of the cone is 27 cm}$

Answer 2

Answer:

c)27cm

Step-by-step explanation:

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