Question The dimensions of a metallic cuboid are 44 cm x 42 cm x 21 cm. It is melted and recast into a sphere. Find the surface area of the 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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Volume of cuboid = (l×b×h)cm²
= (44×42×21)cm²
= 38808cm²
The metallic cuboid is melted and recast to a sphere,
Volume of sphere = Volume of cuboid
Volume of sphere = 38808cm²
Volume of sphere = 4
----πr³
3
=> 4 22
----× ----- r³ = 38808
3 7
=> 4 × r³ = 38808 ÷ 22
---- ----
3 7
=> r³ = 38808 × 7 ÷ 4
---- ----
22 3
=> r³ = 38808 × 7 × 3
---- ----
22 4
=> r³ = 3,528 × 7 × 3
---- ----
2 4
=> r³ = 1,764 × 7 × 3
---- ----
1 4
=> r³ = 441 × 7 × 3
---- ----
1 1
=> r³ = 441 × 7 × 3
=> r³ = 9,261
=> r = ³√9,261
=> r = 21cm
Surface area of sphere = 4πr²
=> 4 × 22 × (21)²
-----
7
=> 4 × 22 × 441
-----
7
=> 38808
----------
7
=> 5544cm²
∴ The surface area of the sphere = 5544cm²