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Probability

Question

Wired Faculty App

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Solution

Let the diameter of the earth be 2r.
Then diameter of the moon =

1 fourth left parenthesis 2 straight r right parenthesis equals straight r over 2

therefore

Radius of the earth =

fraction numerator 2 straight r over denominator 2 end fraction equals straight r

and, Radius of the moon =

equals space 1 half open parentheses straight r over 2 close parentheses equals straight r over 4

therefore space

Surface area of the earth =

4 πr squared

and, Surface area of the moon

equals 4 straight pi open parentheses straight r over 4 close parentheses squared equals 1 fourth space πr squared

Ratio of their surface areas =

fraction numerator Surface space area space of space the space moon over denominator Surface space area space of space the space earth space end fraction

equals fraction numerator begin display style 1 fourth end style πr squared over denominator 4 πr squared end fraction equals 1 over 16 equals 1 space colon space 16

Some More Questions From Probability Chapter

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine:

(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 m² costsर 20.

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of र 7.50 per m².

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?

Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?

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