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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

User Philippe Couronne
by
2.7k points

1 Answer

15 votes
15 votes

Answer:

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.

User Talissa
by
2.6k points