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24 Jun 2021, 08:30
Kudos
Bookmarks
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
History
Date
Time
Result
Not Attempted Yet
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
(A) 125 sq. cm
(B) 200 sq. cm
(C) 600 sq. cm
(D) 400 sq. cm
(E) 800 sq. cm
24 Jun 2021, 10:56
Kudos
Bookmarks
Bunuel
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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