the dimensions of a metallic cuboid are 44 cm *42 cm*21 cm. It is melted and cast into a sphere. what is the radius of this sphere?
Answers
Step-by-step explanation:
As cuboid is melted and cast into a sphere. Substitute the values, Therefore, the radius of sphere is 21.
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The radius of sphere is 21.
Step-by-step explanation:
Given : The dimensions of a metallic cuboid are 44 cm *42 cm*21 cm. It is melted and cast into a sphere.
To find : What is the radius of this sphere?
Solution :
Volume of cuboid is V=l\times b\times hV=l×b×h
Volume of sphere is V=\frac{4}{3}\pi r^3V=
3
4
πr
3
As cuboid is melted and cast into a sphere.
So, Volume of cuboid = Volume of sphere
i.e. l\times b\times h=\frac{4}{3}\pi r^3l×b×h=
3
4
πr
3
Substitute the values,
44\times 42\times 21=\frac{4}{3}\times \frac{22}{7}\times r^344×42×21=
3
4
×
7
22
×r
3
r^3=\frac{44\times 42\times 21\times 3\times 7}{4\times 22}r
3
=
4×22
44×42×21×3×7
r=\sqrt[3]{9261}r=
3
92
r=21