Apill has a shape of a cylinder with a hemisphere at each end. the height of the cylindrical portion is a 12 mm and the overall height is 18 mm.

part A : 453 mm³.

Part B : 2.2 milligrams Vitamin-C per millimeter³

Part C : 214 mg

Step-by-step explanation:

Part (A) :

Volume of the pill = volume of cylinder + 2x volume of two hemispheres

= r²h + 2x ( r³)

Now we know the height of cylinder is 12 mm and radius r = ( 18 - 12 ) = × 6 = 3 mm

So volume of cylinder = π (3)² × (12) = π (9×12) = 108π mm³

Volume of hemisphere = 2 × () π(3)³ = 36π mm³

So volume of the pill =  108π + 36π = 144π = 144 (3.14) = 453 mm³

Volume of the pill would be 453 mm³.

Part B :

If the pill contains 1000 milligrams of Vitamin-C, then per cubic millimeter quantity of Vitamin-C will be

= = = 2.2 milligrams per millimeter³.

The pill contains 2.2 milligrams Vitamin-C per millimeter³

Part C :

Total quantity of Vitamin-C in cylindrical pill = 1000 mg.

Volume of another spherical pill with diameter = 10 mm

Volume of sphere  = = π (10/2)³

                   =  π (5)³

                   =  

                   = 524 mm³

Now this tablet contains Vitamin-C = 1.5 mg per mm³

So amount of Vitamin-C = 524 × 1.5 mg

                                        = 786 mg

So difference in amount of Vitamin-C from cylindrical pill =

1000 - 786 = 214 mg.

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: