Question

*Please Help!*

What is the volume of water, to the nearest tenth of a cubic metre, that would fill this spa tub?

First cylinder= 0.75m diameter, 0.80m height

Cylinder Underneath= 1.25m diameter, 0.70m height

Semi Sphere that holds both cylinders= 3m long

Answer 1

The volume of water that will fill the spa tub is 5.9 cubic meters.

Explanation:

Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)

i. volume of first cylinder =
`\pi`
`r^(2)`h

where r is the radius and h is the height of the cylinder.

r =
`(0.75)/(2)` =
`(3)/(8)`

= 0.375 m

h = 0.80 m

volume of the first cylinder =
`(22)/(7)` x
`((3)/(8) )^(2)` x 0.8

= 0.3536 cubic meters

ii. volume of the cylinder underneath =
`\pi`
`r^(2)`h

r =
`(1.25)/(2)` =
`(5)/(8)`

= 0.625

h = 0.70 m

volume of the cylinder underneath =
`(22)/(7)` x
`((5)/(8)) ^(2)` x 0.7

= 0.8594 cubic meters

iii. volume of the semi sphere =
`(2)/(3)`
`\pi`
`r^(3)`

where r is the radius = 1.5 m

volume of the semi sphere =
`(2)/(3)` x
`(22)/(7)` x
`(1.5)^(3)`

= 7.0714 cubic meters

Thus,

volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)

= 5.8584

The volume of water that will fill the spa tub is 5.9 cubic meters.