Question

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 1

Answer : The correct option is, (A)
`54\pi cm^3`

Step-by-step explanation :

First we have to calculate the volume of cylinder.

Formula used:

Volume of cylinder =
`\pi r^2h`

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 =
`\pi (3cm)^2* (18cm)`

Volume of cylinder =
`162\pi cm^3`

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

Formula used:

Volume of 3 spheres =
`3* (4)/(3)\pi r^3`

Volume of 3 spheres =
`4\pi r^3`

Volume of 3 spheres =
`4\pi (3)^3`

Volume of 3 spheres =
`108\pi cm^3`

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 =
`162\pi cm^3-108\pi cm^3`

Amount of empty space within a cylinder =
`54\pi cm^3`

Therefore, the amount of empty space within a cylinder is,
`54\pi cm^3`