Question

A cone of height 25cm and radius of base 6cm is made up of modelling clay. A child reshapes it in the form of a sphere, the radius of the sphere​

Answer 1

$\sf Given\begin{cases} & \sf{Height\;of\;cone = \bf{25\;cm}} \\ & \sf{Radius\;of\;cone = \bf{6\;cm}} \end{cases}$

To find: Radius of sphere?

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• A child reshapes a cone in the form of a sphere.

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Therefore,

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$:\implies\sf Volume_{\;(sphere)} = Volume_{\;(cone)}$

$:\implies\sf \dfrac{4}{3} \pi r^3 = \dfrac{1}{3} \pi r^2h$

$:\implies\sf \dfrac{4}{3} \times \cancel{\pi} \times r^3 = \dfrac{1}{3} \times \cancel{\pi} \times (6)^2 \times 25$

$:\implies\sf \dfrac{4}{3} \times r^3 = \dfrac{1}{3} \times 36 \times 25$

$:\implies\sf \dfrac{4}{3} \times r^3 = \dfrac{1}{3} \times 900$

$:\implies\sf r^3 = \dfrac{1}{ \cancel{3}} \times 900 \times \dfrac{ \cancel{3}}{4}$

$:\implies\sf r^3 = \cancel{ \dfrac{900}{4}}$

$:\implies\sf r^3 = 225$

$:\implies\sf \sqrt[3]{r^3} = \sqrt[3]{225}$

$:\implies{\underline{\boxed{\frak{\purple{r = 6.082\;cm}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\;radius\;of\;sphere\;is\; {\textsf{\textbf{6.082\;cm}}}.}}}$

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$\qquad\qquad\quad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area\ formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

Answer 2

Answer:

Given :-

• A cone of height is 25 cm and radius of the base is 6 cm is made up of modelling clay.
• A child reshapes it in the form of a sphere.

To Find :-

• What is the radius of the sphere.

Solution :-

Given :

• Height = 25 cm
• Radius = 6 cm

First, we have to find the volume of cone,

We know that,

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

According to the question by using the formula we get,

⇒ $\dfrac{1}{3} {\pi} \times {(6)}^{2} \times 25$

⇒ $\dfrac{1}{3} {\pi} \times 36 \times 25$

➠ $300 {\pi}$ cm³

Now,

Let, the radius of the sphere be r

We know that,

$\boxed{\bold{\large{Volume\: of\: sphere\: =\: \dfrac{4}{3} {\pi}{r}^{3}}}}$

Now, we know that,

✶ Volume of sphere = Volume of cone ✶

According to the question by using the formula we get,

↦ $\dfrac{4}{3}{\pi}{r}^{3} = 300{\pi}$

↦ $\dfrac{4}{3}{r}^{3} = 300$

↦ ${r}^{3} = \dfrac{300 \times 3}{4}$

↦ ${r}^{3} = 75 \times 3$

↦ ${r}^{3} = 225$

↦ $\sqrt[3]{{r}^{3}} = \sqrt[3]{225}$

➥ r = 6.082 cm

$\therefore$ The radius of the sphere is 6.082 cm .