Home
Class 10
MATHS
The external diameter of a conical - cor...

The external diameter of a conical - coronet made off thermocol is 21 cm is length . To wrap up the outer surface of the coronet with foil , the expenditure will be rupees 57.75 at the rate of 10p per -`m^2`. Calculate the height and slant height of the coronet

Text Solution

Verified by Experts

The external diameter of the coronet `21cm`.
`therefore` the external diameter of `" '' "" ''"= (21)/(2)cm`.
Let the slant height of the coronet be 1 cm.
`therefore` the curved surface area `=(22)/(7)xx(21)/(2)xxl ` sq-cm `= 33l` sq-cm.
10 paise `= "rupees" 0.1` is spent to wrap up 1 sq-cm
`"rupees"" '' "" ''"" '' "" '' "" ''"(1xx57.75)/(0.1)`sq-cm`=577.5` sq-cm.
As per question. `33l =577.5 rArr l =(577.5)/(33)=17.5`
Let the height of the coronet be h cm .
`therefore h^2+((21)/(2))^2=(17.5)^2 or , h^2+110.25=306.25or , h^2=306.25-110.25`.
`or h^2=196 or , h=14`.
Hence the height of the coronet is 14 cm and the slant height is 17.5cm.
Promotional Banner

Topper's Solved these Questions

  • RIGHT CIRCULAR CONE

    CALCUTTA BOOK HOUSE|Exercise Exercise 1|25 Videos

  • RIGHT CIRCULAR CONE

    CALCUTTA BOOK HOUSE|Exercise Exercise 2|10 Videos

  • RECTANGULAR PARALLELOPIPED OR CUBOID

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-(MCQs)|40 Videos

  • RIGHT CIRCULAR CYLINDER

    CALCUTTA BOOK HOUSE|Exercise Exercise - 2 (Long-answer type questions)|11 Videos

Similar Questions

Explore conceptually related problems

The external diameter of the base of a right circular cone - shaped wooden toy is 10 cm. The expenditure of colouring the total surface area on the outside of it at the rate of rs 0.07 per sq-cm is rs 19.80 Find the slant height of the toy.

The length of the base diameter of a wooden toy of conical shape uis 10 cm . The expenditure for polishing whole surfaces of the toy at the raye of rupees 2.10 per square - metre is rupees 429. Calculate the height of the toy. Also determine the quantity of wood which is required to make the toy.

The length of the base diameter of a wooden toy of conical shape is 10 cm. The expenditure for polishing whole surfaces of the toy at the rate of Rs. 2.10 perm² is Rs. 429. Calculate the height of the toy and also determine the quantity of wood which is required to make the toy.​

The base area of a right circular cone is 21m and height is 14m . Calculate the expenditure to colour the curved surface at the rate of rs. 1.50 per sq.m.

Height of a hollow right circular cylinder, open at both ends, is 2*8 metres. If length of inner diameter of the cylinder is 4*6 dcm and the cylinder is made up of 84*48 cubic-dcm of iron, then calculate the length of outer diameter of the cylinder.

The quantity of iron - sheet to make a boy a of right circular conical shape is 75(3)/(7) sq-m. if the slant height of it 5 m, then calculate the volume of air in the boya and its height. Determine of the expenditure to colour the whole surface of the boya at the rate of rupees 2.80 per square - metres. [The width of the iron - sheet not to be considered while calculating.]

Water is pouring into a conical vessel of diameter 5.2m. And slant height 6.8 m(as shown in the adjoining ) , at the rate of 1.8 m^(3) per minute .How long will it take to fill the vessel?

A barometer tube is 1 m long and 2 cm^2 in cross section. Mercury stands up to height of 75 cm in the tube. When a small amount of oxygen is introduced in the space above the mercury level,the level falls by 5 cm. Calculate the mass of the oxygen introduced. Room temperature =27^@C g=10 m.s^-2 and density of mercury = 13600 kg.m^-3