Question

Three spheres of copper having the length of 3cm 4cm and 5cm radius are melted and a large sphere is made let us write by calculating the length of radius of the large square

Answer 1

GIVEN :-

• Radius of first sphere, $\sf R_1 = 3 \ cm$

• Radius of second sphere, $\sf R_2= 4 \ cm$

• Radius of third sphere, $\sf R_3 = 5 \ cm$

TO FIND :-

• Radius of large square.

SOLUTION :-

    $\boxed{\bf Volume \ of \ sphere = \dfrac{4}{3}\pi r^3}$

Let the radius of larger sphere be R .

$\bullet \sf \ Volume \ of \ first \ sphere = \dfrac{4}{3}\pi (R_1)^3$

                                    $\sf = \dfrac{4}{3}\times \pi \times 3 \times 3\times 3$

$\bullet\sf \ Volume \ of \ second \ sphere = \dfrac{4}{3}\pi (R_2)^3$

                                        $\sf = \dfrac{4}{3}\times \pi \times 4 \times 4\times 4$

$\bullet\sf \ Volume \ of \ third \ sphere = \dfrac{4}{3}\pi (R_3)^3$

                                      $\sf = \dfrac{4}{3}\times \pi \times 5 \times 5 \times 5$

$\bullet\sf \ Volume \ of \ larger \ sphere = \dfrac{4}{3}\pi (R)^3$

According to the question,

Volume of larger sphere = Volume of first sphere + Volume of second

                                              sphere + Volume of third sphere

$\longrightarrow\sf \dfrac{4}{3} \pi \times R^3 = \left(\dfrac{4}{3}\pi \times 3\times 3 \times 3\right)+\left(\dfrac{4}3}\pi \times 4 \times 4 \times 4\right)+\left(\dfrac{4}{3}\pi \times 5\times 5 \times 5 \right)\\\\\longrightarrow \dfrac{4}{3}\pi \times R^3 =\dfrac{4}{3}\pi [( 3\times 3\times 3 )+(4\times 4\times 4)+(5\times 5 \times 5 )]\\\\\longrightarrow R^3 = 27+64+125 \\\\\longrightarrow R^3 = 216 \\\\\longrightarrow\bf R = 6$

Radius of larger sphere = 6 cm