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605-655 (Medium)|   Geometry|      
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Bunuel
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Find the surface area of the biggest cube that can completely fit ins 24 Jun 2021, 08:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

50% (01:37) correct 50% (02:02) wrong based on 18 sessions

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Find the surface area of the biggest cube that can completely fit inside a sphere of radius 10 cm.

(A) 125 sq. cm
(B) 200 sq. cm
(C) 600 sq. cm
(D) 400 sq. cm
(E) 800 sq. cm
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E
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Find the surface area of the biggest cube that can completely fit ins 24 Jun 2021, 10:56
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Bunuel
Find the surface area of the biggest cube that can completely fit inside a sphere of radius 10 cm.

(A) 125 sq. cm
(B) 200 sq. cm
(C) 600 sq. cm
(D) 400 sq. cm
(E) 800 sq. cm
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Solution :
We are given,
• Radius of the sphere = 10cm
We need to find the surface area of the largest cube inscribed in the sphere.

From the diagram below, it is clear that :
Diagonal of the cube = diameter of the sphere
⟹ \(\sqrt{3}\)a = 2r (where a is the length of side of the cube and r is the radius of the sphere)
⟹ a = \(\frac{2r}{\sqrt{3}}\)
⟹ a = \(\frac{20}{\sqrt{3}}\) (∵ r = 10 cm)

Therefore surface area of the cube = 6\(a^{2}\)
= 6 * \( (\frac{20}{\sqrt{3}})^2\)
= \(6 * \frac{400}{3}\)
= 800 sq. cm

Therefore, the correct answer is Option E.
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