Q. 95.0( 3 Votes )

# A tent is made in the form of a conic frustum, surmounted by a cone. The diameters of the base and top of the frustum are 14m and 7 m and its height is 8 m. The height of the tent is 12m. Find the quantity of canvas required. [Take π=22/7]

Answer :

For the lower portion of the tent:

Diameter of the base = 14 m

Radius, R, of the base = 7 m

Diameter of the top end of the frustum = 7 m

Radius of the top end of the frustum =

Height of the frustum = h = 8 m

Slant height = l = √{h^{2} + (R – r)^{2}}

= √{(8)^{2} +(7 – 3.5)^{2}

= √64 + (3.5)^{2}

= √64 + 12.25

= √76.25

= 8.73 m

For the conical part

Radius of the cone base = r = 3.5 m

Height of the cone = Height of the tent – height of frustum

= 12 – 8

= 4 m

Slant height of cone = L = √(4)^{2}+(3.5)^{2}

= √16 + 12.25

=√28.25

= 5.3 m

Total quantity of canvas = CSA of frustum + CSA of conical top

= πl(R + r) + πrL

= π [8.73(7 + 3.5) + 3.5 × 5.3]

= 346.5 m^{2}

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PREVIOUSA bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs. 20 per litre and the cost of metal sheet used if it costs Rs. 10 per 100cm2. [Use π=3.14]NEXTAn oil funnel of tin sheet consists of a cylindrical portion 8 cm along attached to a frustum of a cone. If the total height be 15cm, the diameter of the cylindrical portion 1 cm and diameter of the top of the funnel 10cm, find the area of the tin required. [Take π=22/7]

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