Q50 of 56 Page 13

In Fig. 16.74, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (CBSE 2015)

In triangle ABC and ADE,


DE||BC


So, ∆ABC ~ ∆ADE




⇒ OE = 2cm



let slant height be l


Slant height, l =



⇒ l = 13.42cm


Total surface area of the frustum = πr(r + l)


= π × 6(6 + 13.42)


= 366.21 cm2


Now, for smaller cone:


Slant height, l’ =


⇒ l = 4.472 cm


So, curved surface area of smaller cone = πrl


= π × 2 × 4.472 = 28.11 cm2


Now, total surface area of the remaining frustum = total surface area of the bigger cone – curved surface area of smaller cone + area of base of smaller cone


= 366.21 – 28.11 + π (2)2


= 350.52 cm2

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48

Water is flowing at the rate of 2.52 km / h through a cylindrical pipe into a cylindrical tank, the radius of the base is 40 cm. If the increase in the level of water in the tank, in half and hour is 3.15 m, find the internal diameter of the pipe. (CBSE 2015)

 49

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is . Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of ` 10 per cm2. (CBSE 2015)

 51

Due to heavy floods in a State, thousands were rendered homeless. 50 schools collectively offered to the State Government to provide place and the canvas for 1, 500 tents to be fixed by the Government and decided to share the whole expenditure equality. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs. 120 per sq. m, find the amount shared by each school to set up the tents.

What value is generated by the above problem? (Use π = 22/7)(CBSE 2016)

 52

in Fig. 5, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs. 500/sq. metre. (Use π = 22/7)

(CBSE 2016)