Question

a right circular metalic cone of height 20cm and base radius 5cm is melted and recast into a solid sphere find the radius of the sphere​

Answer 1

Given:

• A cone has a height 20cm and base radius 5cm
• And its later melted into a solid sphere

To Find:

• The measure of the radius of the sphere

Solution:

As we have been provided with the height and radius of the cone and said that wee have to find the radius of the sphere let's use suitable formulae to find the required solution

${\underline{\bf{\bigstar{According \; to \; the \; question:}}}}$

• A cone is recast into a sphere so, the volume of the cone will be equal to the volume of the sphere

→ The formula to find the volume of a cone is,

$\longrightarrow \tt Volume \; of \; a \; cone = \pi r^{2} \dfrac{h}{3}$

→ The formula to find the volume of a sphere is,

$\longrightarrow \tt Volume \; of \; a \; sphere = \dfrac{4}{3} \pi r^3$

★ Now as we know that the the radius and height of the cone are 5cm and 20cm let's frame an equation substituting them in the formula which is equal to the volume of the sphere

$\longrightarrow \tt \pi r^2 \dfrac{h}{3} = \dfrac{4}{3} \pi r^3$

$\longrightarrow \tt \pi (5)^2 \times \dfrac{20}{3} = \dfrac{4}{3}\pi r^3$

$\longrightarrow \tt \pi \dfrac{25 \times 20}{3}= \dfrac{4}{3} \pi r^3$

$\longrightarrow \tt \pi \dfrac{500}{\cancel3} = \dfrac{4}{\cancel3} \pi r^3$

$\longrightarrow \tt 500\cancel\pi = 4\cancel\pi r^3$

$\longrightarrow \tt 500 = 4r^2$

$\longrightarrow \tt r^3 = \cancel\dfrac{500}{4}$

$\longrightarrow \tt r^3 = 125$

$\longrightarrow \tt r = \sqrt[\tt 3]{\tt 125}$

$\longrightarrow {\purple{\underline{\boxed{\pmb{\frak{R = 5cm }}}}\bigstar}}$

Hence:

• The measure of  radius of the sphere is 5cm

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