wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Three solid spheres of gold whose radii are 1 cm, 6 cm and 8 cm, respectively are melted into a single solid sphere. Find the radius of the sphere.

Open in App
Solution

Given that,
Three solid spheres have radii 1 cm, 6 cm and 8 cm, respectively.
A single solid sphere is made by melting the three spheres.

To find out,
The radius of the new sphere.

Let the radius of the new sphere be x cm
We know that, when one solid is constructed by melting one or more objects, the volume remains same.
Hence, volume of new sphere = sum of volumes of the three sphere.

We know that, volume of a sphere =43πr3

Hence, 43πx3=43π(1)3+43π(6)3+43π(8)3

x3=(1)3+(6)3+(8)3

x3=1+216+512

x3=729

x3=9×9×9

x3=93

x=9 cm

Hence, the radius of the new sphere is 9 cm.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Volume of Solids
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon