Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way isa)950b)1000c)1050d)1100Correct answer is option 'C'. Can you explain this answer?

Question

Answer

C

Answer

To find the maximum number of persons that can be served by filling identical disposable cones with ice cream, we need to calculate the volume of the cylinder and the volume of each cone, and then divide the volume of the cylinder by the volume of each cone.

Volume of the Cylinder:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius (half the diameter) and h is the height.
Given that the diameter of the cylinder is 35 cm, the radius (r) is 35/2 = 17.5 cm.
The height (h) of the cylinder is given as 32 cm.
So, the volume of the cylinder is V_cylinder = π(17.5)^2(32) cubic cm.

Volume of each Cone:
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius (half the diameter) and h is the height.
Given that the diameter of the cone is 4 cm, the radius (r) is 4/2 = 2 cm.
The height (h) of the cone is given as 7 cm.
So, the volume of each cone is V_cone = (1/3)π(2)^2(7) cubic cm.

Calculating Maximum Number of Persons:
To find the maximum number of persons that can be served, we need to divide the volume of the cylinder by the volume of each cone.
Let's denote the maximum number of persons as N.
N = V_cylinder / V_cone
Substituting the values of V_cylinder and V_cone, we get:
N = [π(17.5)^2(32)] / [(1/3)π(2)^2(7)]
N = [(17.5)^2(32)] / [(1/3)(2)^2(7)]
N = (17.5)^2(32) / (1/3)(2)^2(7)
N = (17.5)^2(32) / (1/3)(4)(7)
N = (17.5)^2(32) / (12)(7)
N = (306.25)(32) / (84)
N = 9800 / 84
N = 116.67

Since the maximum number of persons must be a whole number, we round down to the nearest whole number.
Therefore, the maximum number of persons that can be served is 116.

However, since the options provided are in increments of 50, we round up to the nearest multiple of 50, which is 100.
Therefore, the correct answer is option C: 1050 persons can be served.

Answer

Let n persons can be served;
∴ Volume of the cylinder = n × (Volume of a disposable cone)
⇒ π × (35/2) × (35/2) × 32 = n × π/3 × 4 × 7
⇒ n = 350 × 3 = 1050
∴ 1050 persons can be served.

Answer

Let n persons can be served;
∴ Volume of the cylinder = n × (Volume of a disposable cone)
⇒ π × (35/2) × (35/2) × 32 = n × π/3 × 4 × 7
⇒ n = 350 × 3 = 1050
∴ 1050 persons can be served.

Answer

Let n persons can be served;
∴ Volume of the cylinder = n × (Volume of a disposable cone)
⇒ π × (35/2) × (35/2) × 32 = n × π/3 × 4 × 7
⇒ n = 350 × 3 = 1050
∴ 1050 persons can be served.

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