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Probability

Question

Wired Faculty App

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

Solution

Let the radius of base of hemisphere and cone, each be r cm. Let the height of the cone be h cm.
Volume of the cone =

1 third πr squared straight h space cm cubed

Volume of the hemisphere =

2 over 3 πr cubed space cm cubed

Acording to the question,

1 third πr squared straight h equals 2 over 3 πr cubed

⇒ h = 2r
⇒ Height of the cone = 2r cm.
Height of the hemisphere = r cm.
∴ Ratio of their heights = 2r : r = 2 : 1.

Some More Questions From Probability Chapter

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?

A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

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