The base radii of the two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.

Solution

Let the base radii of the two right circular cones be 3x and 5x respectively.
Let their common height be h. Then,
Volume of the first cone (v₁) = $1 third πr squared straight h$

   $equals 1 third straight pi left parenthesis 3 straight x right parenthesis squared straight h$
and, volume of the second cone (v₂) = $apostrophe 1 third πr squared straight h apostrophe$
   $equals 1 third straight pi left parenthesis 5 straight x right parenthesis squared straight h$
$therefore$ Ratio of their volumes
$equals straight v subscript 1 over straight v subscript 2 equals fraction numerator begin display style 1 third end style straight pi left parenthesis 3 straight x right parenthesis squared straight h over denominator begin display style 1 third end style straight pi left parenthesis 5 straight x right parenthesis squared straight h end fraction equals 9 over 25 equals 9 colon 25.$

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Probability

The base radii of the two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.

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 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?

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.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m².

Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.

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For Daily Free Study Material Join wiredfaculty

Probability

The base radii of the two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.

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 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?

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.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m2.

Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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?

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m².