VOLUME AND SURFACE AREA (revision-1)

VOLUME AND SURFACE AREA (revision-1)

Q1. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and diameter 6 cm ,having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream .

Q 2. Two solid right circular cones have the same height. the radii of their bases are r1 and r2. They are melted and recast into a cylinder of same height. Find the radius of the base of the cylinder .

Q3. Water flows at the rate of 10 metres per minute through a cylinder pipe 5mm in diameter . how long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm ? (Ans= 51 minutes 12 seconds)

Q4. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm,a conical cavity of same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2. ( Ans = 18 cm 2)

 Q5. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots,each of which is a sphere of radius 0.5 cm are dropped into the vessel,one-fourth of the water flows out. Find the number of lead shots dropped in the vessel. (Ans = 100 )

 Q6. Water in a canal 6 m wide and 1.5 m deep, is flowing with a speed of 10Km/h .How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed ? ( Ans = 56.25 hectares)

 Q7. A copper wire,3 mm in diameter , is wound about a cylinder whose length is 12 cm, and diameter 10 cm,so as to cover the curved surface area of the cylinder.Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm2. ( Ans = 125.6 m ,111.533 Kg)

Q 8. If the radii of the circular ends of a conical bucket which is 45 cm high, are 28 cm and 7 cm. Find the capacity of the bucket.

Q 9. The perimeters of the ends of a frustum are 48 cm and 36 cm . If the height of the frustum be 11 cm , find its volume.

Q10. A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of itslower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fil the container at the rate of Rs. 15 per litre and the cost of metal sheet used , If the cost is Rs 5 per 100 cm2 (Ans: Rs. 156.75, Rs 97.96(approx.))

Q11. The radii of the circular ends of a frustum of a cone of height 6cm are 14 cm and 6 cm respectively. Find the lateral surface area and the total surface area of the frustum. (Ans: 628.57 cm2,1357.71 cm2)

Q12. A friction clutch is in the form of a frustum of a cone, the diameter of the ends being 32 cm and 20 cm and length 8 cm. Find its bearing surface and volume . (Ans: 817.14 cm2,4324.57 cm3)

Q13. The slant height of the frustum of a cone is 4 cm , and the perimeter of its circular bases are 18 cm and 6 cm respectively. Find the surface area of the frustum. (Ans: 48 cm2)