Question

The length of the largest possible rod that can
be placed in a cubical room is 35 3 m. What
is the surface area of the largest possible
sphere that fit within the cubical room.
(A) 3500 m^2 (B) 3850 m^2
(C) 2450 m^2 (D) none of these

Answer 1

largest possible rod would go from corner to opposite corner. figure out the length of the side of the cube with the measurement from corner to opposite corner of 353m. Then the radius of the sphere will be half of this. Plug that into the surface area of a sphere formula and get the answer.

Answer 2

By using the formula, surface area of a sphere= 4*3.14* (radius)^2, I got 3912 as the approx surface area. So, shall I approximate it to (b) or choose opton(d) itself?

Answer 3

what did you get for the side length of the cube?

Answer 4

Side length is 3.53 but I took 35.3 and divided it by 2. Now, I am correcting the answer. Will post it soon.

Answer 5

I am extremely sorry. The side length of cube is 35 root 3 metres. Accordingly, I am trying to correct my answer.

Answer 6

if corner to corner is \[35\sqrt{3}\]then the length of a side is 35.

Answer 7

How did u get that?

Answer 8

first get the diagonal of a face:\[\sqrt{s^2+s^2}=\sqrt{2s^2}=\sqrt{2}s\]

Answer 9

then the diagonal to diagonal distance is the hypotenuse of a triangle with one side that is the face diagonal, and one that is another side. \[\sqrt{2s^2 + s^2}=\sqrt{3s^2}=\sqrt{3}s\]

Answer 10

I mean "corner to opposite corner" not "diagonal to diagonal"

Answer 11

So, am I to calculate like this?
S.A. of sphere= 4*3.14*r^2=4*3.14*17.5*17.5=3846.5 approx to 3850. which is option(b)?

Answer 12

Yes!

Answer 13

Thanks a lot!!