A sphere is inscribed inside a cube. The volume of the cube is 1728 $\text{cm}^3$ . What is the total surface area of the sphere?
A sphere is inscribed inside a cube. The volume of the cube is 1728 $\text{cm}^3$ . What is the total surface area of the sphere?
एक गोले को एक घन के अंदर अंकित किया गया है। घन का आयतन $1728\text{सेमी}^3$ हैं। गोले का कुल पृष्ठीय क्षेत्रफल कितना हैं?
Detailed Solution & Logic
144 $\pi\text{cm}^2$/ 144 $\pi\text{सेमी}^2$
Volume of cube = $1728 \text{ cm}^3$
So, side of cube = $12$ cm (because $12^3 = 1728$)
Sphere is inscribed in cube ⇒ diameter of sphere = side of cube
So, radius = $6$ cm
Surface area of sphere = $4\pi r^2$
$= 4\pi \times 6^2$
$= 4\pi \times 36$
$= 144\pi \text{ cm}^2$
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