1. A cube and a sphere are of the same height. Find the ratio of their volume.
2. Pind the arithmetic mean of first-five natural numbers.
3. A die is thrown. What is the probability of getting a multiple of 3 on the upper face?
4. Diagonals of a quadrilateral ABCD bisect each other. If LA = 35º, determine 2B.
SETAN.
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Answer:
The sphere will have the diameter equal to the side of the cube as they are of the same height.
If the length of the side of the cube is a, then the diameter of the sphere =a unit
∴ Radius of the sphere =
2
a
Volume of a sphere of radius 'r' =
3
4
πr
3
Hence, volume of this sphere =
3
4
×π×(
2
a
)
3
=
6
πa
3
Volume of a cube of edge a =a
3
Ratio of their volumes
=
6
πa
3
:a
3
=
6
π
:1
=
7×6
22
:1
=
7×3
11
:1
=11:21
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