Find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (Volume of a sphere =43πr3) A. 54π cm3 B. 72π cm3 C. 126π cm3 D. 378π cm3

Answer : The correct option is, (A)

Step-by-step explanation :

First we have to calculate the volume of cylinder.

Formula used:

Volume of cylinder =

where,

r = radius = 3 cm

h = height = 18 cm   (We are assuming that 3 solid spheres stacked to each other = 3 × diameter of each sphere = 3 × 2 × 3 = 18)

Volume of cylinder =

Volume of cylinder =

Now  we have to calculate the volume of 3 solid spheres.

Formula used:

Volume of 3 spheres =

Volume of 3 spheres =

Volume of 3 spheres =

Volume of 3 spheres =

Now we have to calculate the amount of empty space within a cylinder.

Amount of empty space within a cylinder = Volume of cylinder - Volume of 3 spheres

Amount of empty space within a cylinder =

Amount of empty space within a cylinder =

Therefore, the amount of empty space within a cylinder is,

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

1/800 is the right answer