Really need help. please

daoud

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Nov 22, 2014
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Hello. Everyone. I am was doing some work and stumbled upon this.

Part (a): Given: an open rectangular fish tank with base 20 cm by 30 cm, currently containing 9,600 cm^3 of water.

i) State the number of litres of water in the tank.
ii) Calculate the depth of water in the tank.
iii) Calculate the total surface area of the tank which is in contact with the water.
iv) The water entered the tank through a circular pipe of radius 0.8 cm. It flowed through the pipe at 25 cm per second. How long did the 9,600 cm^3 of water take to enter the tank? (Give your answer to the nearest whole second.)

Part (b): Two hundred fifty identity spheres are placed in the bottom of the tank. Each sphere has a volume of 2.6 cm^3. [Recall that the volume V of a sphere with radius r is given by V = (4/3)(pi)(r^3).]

i) Calculate how much the water level in the tank will rise. (Give your answer in millimetres.)
ii) Calculate the radius of one of these spheres.


I seem to do it my way, but the answers is somewhat wrong.. Now I'm not sure of the answers is wrong or what? So please solve this problem for me. Its just the past A IV and B 1. Thanks I will highly appreciate any help .
 
Last edited by a moderator:
Hello. Everyone. I am was doing some work and stumbled upon this.

Part (a): Given: an open rectangular fish tank with base 20 cm by 30 cm, currently containing 9,600 cm^3 of water.

i) State the number of litres of water in the tank.
ii) Calculate the depth of water in the tank.
iii) Calculate the total surface area of the tank which is in contact with the water.
iv) The water entered the tank through a circular pipe of radius 0.8 cm. It flowed through the pipe at 25 cm per second. How long did the 9,600 cm^3 of water take to enter the tank? (Give your answer to the nearest whole second.)

Part (b): Two hundred fifty identity spheres are placed in the bottom of the tank. Each sphere has a volume of 2.6 cm^3. [Recall that the volume V of a sphere with radius r is given by V = (4/3)(pi)(r^3).]

i) Calculate how much the water level in the tank will rise. (Give your answer in millimetres.)
ii) Calculate the radius of one of these spheres.


I seem to do it my way, but the answers is somewhat wrong.. Now I'm not sure of the answers is wrong or what? So please solve this problem for me. Its just the past A IV and B 1. Thanks I will highly appreciate any help .

What are your thoughts?

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Part (a): Given: an open rectangular fish tank with base 20 cm by 30 cm, currently containing 9,600 cm^3 of water.

i) State the number of litres of water in the tank.
How many millilitres per cubic centimetre? How many millilitres per litre? Do the conversion.

ii) Calculate the depth of water in the tank.
What is the cross-sectional area of the base? Given that volume and that cross-sectional area, what must be the depth?

iii) Calculate the total surface area of the tank which is in contact with the water.
Given the width, length, and depth of the "brick" of water, what are the areas of each of the sides? What then is the total area?

iv) The water entered the tank through a circular pipe of radius 0.8 cm. It flowed through the pipe at 25 cm per second. How long did the 9,600 cm^3 of water take to enter the tank?
What is the cross-sectional area of the pipe? Think of the water that has flowed through the pipe in one second as a right circular prism. What is the "height" of that prism, given the rate of flow per second? What then is the volume of the prism? Given this per-second volume of flow, how long did it take to obtain the given total volume?

Part (b): Two hundred fifty identity spheres are placed in the bottom of the tank. Each sphere has a volume of 2.6 cm^3. [Recall that the volume V of a sphere with radius r is given by V = (4/3)(pi)(r^3).]

i) Calculate how much the water level in the tank will rise.
What is the total volume of the spheres? What then is the total water-plus-sphere "brick" volume inside the tank? (We are assuming, of course, that the water covers the spheres.) Given that the cross-sectional area of the base has not changed, what must be the new height of the "brick"?

ii) Calculate the radius of one of these spheres.
You are given the volume V of a sphere and the formula for the volume V in terms of the radius r. You are asked for the value of the radius r. Plug the given volume into the given formula. Solve for the specified variable.

I seem to do it my way, but the answers is somewhat wrong.
What did you do? What were your answers?

Please be complete, as we cannot check work we cannot see. Thank you! :wink:
 
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