Question

Three spheres of diameter 6cm, 8cm and 10cm are melted and formed a single sphere. Find the diameter of the sphere. [ans: 12cm]

Answer 1

GIVEN:

• Diameter of three spheres are 6cm, 8cm and 10cm respectively.

TO FIND:

• What is the diameter of new sphere ?

SOLUTION:

❍ Radius = $\sf{\dfrac{Diameter}{2}}$

✒ Radius of first sphere = 3 cm

✒ Radius of second sphere = 4 cm

✒ Radius of third sphere = 5 cm

To find the volume of sphere, we use the formula:-

$\large{\boxed{\bf{\star \: V = \dfrac{4}{3} \pi r^3 \: \star}}}$

❮ Volume of 3 spheres = Volume of new sphere❯

According to question:-

$\bf{\star V = \dfrac{4}{3} \pi (3)^3 + \dfrac{4}{3} \pi (4)^3 + \dfrac{4}{3} \pi (5)^3 = \dfrac{4}{3} \pi r^3\: \star}$

$\rm{\longrightarrow V = \dfrac{4}{3} \pi (27 + 64 + 125) = \dfrac{4}{3} \pi r^3}$

$\rm{\longrightarrow 216 = r^3 }$

$\rm{\longrightarrow \sqrt{216} = r }$

$\bf{\longrightarrow r = 6 cm}$

$\bf{\star \: DIAMETER = 2R \: \star}$

$\rm{\longrightarrow D = 2 \times 6 }$

$\bf{\longrightarrow DIAMETER = 12 cm }$

❝ Hence, the volume of sphere is 12 cm ❞

______________________

Answer 2

Answer:

Diameter of new sphere = 12 cm

Step-by-step explanation:

volume of sphere = 4/3 ×pi × r^3

volume of first sphere = 4÷3 × 3.142 × 3,×3÷3 = 113.1 cc

volume of second sphere = 4÷3 × 3.142 × 4×4×4 = 268.08 cc

volume of third sphere = 4÷3 × 3.142 × 5×5×5 = 523.6 cc

Volume of new sphere = sum of volumes of three spheres

= 113.1 + 268.08 + 523.6 = 904.78 cc

volume of sphere = 4÷3 ×pi × r^3

r^3 = volume of sphere ÷ ( 4÷3×pi)

=904.78 ÷( 4÷3 ×pi )

=904.78 ÷ ( 4÷3 × 3.142)

= 215.97 cc

r = cuberoot 215.97

= 5.99972220936

OR

= 6 cm

diameter of new sphere

= 2× r

= 12 cm