## Step 6: Applications of the Volume formula.

PROBLEM 1)

Imagine you are in the 16th century. Italy. Sitting at the desk of Galileo Galilei. Galileo has given you the task of finding out the volumes of certain planets. He has provided you with the radii of those planets. They are as follows:

Mercury-----2,440,000 metres.

Venus------ 6,051,000 metres.

Mars ----- 11145013.12 feet.

Jupiter----- 78184601.92 yards.

Galileo wants all answers in terms of cubed metres . What answers will you give Galileo?

SPOILER: Watch out for Mars and Jupiter!

ANSWER:

Well, since we know the radii ...the problem becomes very simple!

The Answers are:

Mercury---------6.085 multiplied by 10 raised to the power 19.

Venus----------9.28 multiplied by 10 raised to the power 20.

Mars------------1.642 multiplied by 10 raised to the power 20.

Jupiter--------- 1.5306 multiplied by 10 raised to the power 24.

(All values are in cubed metres.)

PROBLEM 2)

I have to build a semi- spherical planetarium inside a huge room of volume 63,000 cu.metres. The diameter of the planetarium should be 50 metres. Will my planetarium fit inside the room?

ANSWER: Remember that the planetarium is SEMI-spherical. So it's volume is half the volume that we calculate for a sphere. Half the sphere will quite easily fit inside the room.

Volume of the planetarium=32724.92 cu.metres.

PROBLEM 3) Imagine that one day Mr. Gates, the millionaire goes mad and decides to fund a project in which the moon is to be opened up and completely filled with marbles having circumference 2metres. Now the radius of the moon is 1,738,000 metres. Approximate how many marbles will fit into the moon till the moon fills up completely!

ANSWER:

The no. of marbles =(volume of the moon) divided by (volume of each marble).

And radius = (circumference)/ 2*PI

Volume of each marble= 0.1351 cu.metres

Volume of the moon =2.199 multiplied by 10 raised to the power 19.

The no. of marbles =1.6277 multiplied by 10 raised to the power 20!!!

NOTE: Given below, are the tables which summarize all that we have already examined in the steps prior to this one. They may prove to be useful in solving the above problems.

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