Question

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Initially the rectangular prism on the left was full of water. Then water was poured in the right cylindrical container so that the heights of water in both containers are equal. Find the height h of water in both containers.(round your answer to the nearest tenth of a cm).
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Answer 1

Answer:

Solution:

The volume of water in the rectangular prism in the left is given by

2\times4\times10 = 80 cm^32×4×10=80cm

3

The volume of water in the middle rectangular prism in given by

2\times4\times h = 80 h2×4×h=80h

The volume of water in cylinder on the right is given by

\pi\times (1)2\timesh = \pi \times h , \pi = 3.14π×(1)2\timesh=π×h,π=3.14

Since all water in the container on the left is poured in both containers on the right, then

80 cm^3 = 8 h + \pi\times h80cm

3

=8h+π×h

Solve to find h

h = \frac{80}{(8 + \pi)}h=

(8+π)

80

\text{ value of }\pi =3.142 value of π=3.142

On substituting the value we get,

h = \frac{80}{(8 + 3.142)}=\frac{80}{11.142}=7.18 cmh=

(8+3.142)

80

=

11.142

80

=7.18cm

h = 7.2 cm (rounded to the nearest tenth of a cm).

Hope it was helpful.