Q8 of 24 Page 227

The length of the base diameter of a wooden toy of the conical shape is 10cm. The expenditure for polishing the whole surfaces of the toy at the rate of ₹2.10 per m2 is ₹429. Let us calculate the height of the toy. Let us also determine the quantity of wood which is required to make the toy.

Let, whole surface area of the toy = x m2


According to problem,


⇒ x × 2.1 = 429


⇒ x = 429/2.1


⇒ x = 204.286


Base diameter of the toy = 10 cm


∴ base radius of the toy, r = 10/2 = 5 cm


Let, slant height = l cm


According to problem,


⇒ πr2 + πrl = 204.286


⇒ 22/7(52 + 5l) = 204.286


⇒ 5l + 25 = 65


⇒ 5l = 40


⇒ l = 8


∴ slant height = 8 cm


∴ height = √(l2 – r2)= √(82 – 52) = √(64 – 25) = 6.24 cm


∴ Volume of the toy,


= πr2h/3


= 22/7 × 52 × 6.24/3


= 163.43 m3


∴ Quantity of wood required to make the toy = 163.43 m3


More from this chapter

All 24 →
6

77sq.m. tripal is required to make a right circular conical tent. If the slant height is 7m. Then let us write by calculating, the base area of the tent.

 7

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

 9

The quantity of iron sheet to make boya of right circular conical shape is m2. If the slant height of it is 5m, then let us write, by calculating, the volume of air in the boya and its height. Let us determine the expenditure to colour the whole surface of the boya at the rate of ₹2.80 per m2. [The width of the iron-sheet not to be considered while calculating.]

10

In a right circular conical tent 11 persons can stay. For each person 4m2 space in the base and 20m3 air are necessary. Let us determine the height of the tent put up exactly for 11 persons.