Question

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Answer 1

Answer:

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

Step-by-step 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 = $\frac{0.75}{2}$ = $\frac{3}{8}$

 = 0.375 m

h = 0.80 m

volume of the first cylinder = $\frac{22}{7}$ x $(\frac{3}{8} )^{2}$ x 0.8

                                        = 0.3536 cubic meters

ii. volume of the cylinder underneath = $\pi$$r^{2}$h

r = $\frac{1.25}{2}$ = $\frac{5}{8}$

 = 0.625

h = 0.70 m

volume of the cylinder underneath = $\frac{22}{7}$ x $(\frac{5}{8}) ^{2}$ x 0.7

                                                      = 0.8594 cubic meters

iii. volume of the semi sphere = $\frac{2}{3}$ $\pi$$r^{3}$

where r is the radius = 1.5 m

volume of the semi sphere = $\frac{2}{3}$ x $\frac{22}{7}$ 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.