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Solution - A Solid Iron Pole Having Cylindrical Portion 110 Cm High and of Base Diameter 12 Cm is Surmounted by a Cone 9 Cm High. Find the Mass of the Pole, Given that the Mass of 1 Cm3 of Iron is 8 Gm. - CBSE Class 10 - Mathematics

Question

A solid iron pole having cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that the mass of 1 cm3of iron is 8 gm.

Solution

Let r1 cm and r2 cm denate the radii of the base of the cylinder and cone respectively. then,

r1 = r2 = 12/2 = 6 cm

let h and l cm be the heights of the cylinder and the cone respectively Then,

h = 110cm and l = 9cm

∴ volume of the cylinder = `pir_1^2h cm^3`

= π x 6 x 6 x 110 cm3

of the cone = `1/3pir_2^2l  cm^3`

`1/3xxpixx6xx6xx9`

∴ Total volume of the iron = volume of the cylinder + volume of the cone 

= π x 6 x 6 x 110 +1/3 x π x 6 x 6 x 9

= π x 36`((330+9))/3`

= π x 12 x (330+9)

= `22/7xx12xx339`

= 12785.14 cm3

Mass of 1 cm3 of iron is 8 gm.

Therefore mass of the iron

= 12785.14 x 8 gm

= 102281.18

102.28 kg.

Hence, the mass of pale is 102.28 kg.

 

 

  Is there an error in this question or solution?

APPEARS IN

 R.D. Sharma 10 Mathematics (with solutions)
Chapter 16: Surface Areas and Volumes
Q: 21

Reference Material

Solution for question: A Solid Iron Pole Having Cylindrical Portion 110 Cm High and of Base Diameter 12 Cm is Surmounted by a Cone 9 Cm High. Find the Mass of the Pole, Given that the Mass of 1 Cm3 of Iron is 8 Gm. concept: Volume of a Combination of Solids. For the course CBSE
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