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Oliveboard Question of the day

Question: A cylindrical container of height 15 cm and base diameter 24 cm contains oil. This oil is to be transferred to 5 similar conical cans and 6 similar spherical cans. The radii of the spherical cans is 5 cm. If the diameter of the base of the conical cans is 8 cm, find the height of the conical cans.
(1) 52.5 cm
(2) 47.5 cm
(3) 43.5 cm
(4) 49.5 cm
(5) 51.5 cm

 

Solution posted below. Click on the plus sign to view the solution.

Answer and Explanation

Answer key: 3

 

Total volume of oil = πr2h = π x 144 x 15 = 2160 π cm3

Let the height of each conical can be h.

Total vol of 6 spherical cans and 5 conical cans = vol of cylindrical can.

6 x (4/3 x π x 125) + 5 x (1/3 x π x 4 x 4 x h) = 2160 π

1000 + 80/3 h = 2160

80/3 h = 1160

h = 43.5 cm

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