A cast-iron pipe has an external diameter of 75 mm. If it is 4.2 m long, find the area of the outer surface.   \(\left[ Assume\pi =\frac { 22 }{ 7 } \right] \)      

4

(a)

Find the curved surface area of a closed cylindrical petrol storage tank that is 3.8 m in diameter and 4.9 m in height.

4

(a)

The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.

4

(a)

Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.

4

(a)

A hemispherical bowl made of steel is of 1 cm thickness. The inner radius of the bowl is 6 cm. Find the total surface area of the bowl, in terms of \(\pi .\)

4

(a)

The surface area of a sphere of radius 5 cm is 5 times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

4

(a)

Find the length of the longest rod that can be placed in a room 12 m \(\times\) 9 m \(\times\) 8 m.

4

(a)

If v is the volume of a cuboid of dimensions a, b and s is its surface area, then prove that \(\frac{1}{v}=\frac{2}{s}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\)

4

(a)

The areas of three adjacent faces of a cuboid are p, q and r. If its volume is v, prove that v² = pqr

4

(a)

A hemispherical bowl is made of 0.2 cm thick steel. the inner diameter of the bowl is 8 cm. Also, find outer curved surface area of the bowl. also, find the cost of polishing its outer surface at the rate of Rs 2 per cm³ (Take \(\pi\)=\(\frac { 22 }{ 7 } \))

4

(a)