Surface area and volume

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

• 912

• 769

• 858

• 465

If the ratio of the radius of a cone and a cylinder of equal volume is 3:5 , then find the ratio of their heights

• 25/3

• 28/3

• 23/3

• 7

A solid metallic sphere of diameter 21cm is melted and recast into a number of smaller cones of diameter 3.5cm and height 3 cm. The number of cones so formed is

• 254

• 504

• 540

• 405

A bucket is in the form of a frustum of a cone, its depth is 15 cm ans the diameters of the top and the bottom are 56cm and 42 cm respectively. How many liters of water can the bucket hold?

• 28.49

• 7.5

• 2.5

• 10

A 20m deep well of dia 7m is dug and the earth taken out is evenly spread out to form a platform of 22m by 14m. Find the height of the platform (in m)

• 7.5

• 2.5

• 10

• 5

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

• 256500

• 526500

• 625500

• 562500

The diameter of a sphere is 6 cm. Its melted and down into a wire of diameter 2mm. The length of wire is

• 66m

• 36m

• 18m

• 12m

The lateral surface area of a right circular cone of height 28cm and base radius 21cm (in sqcm) is

• 2310

• 2110

• 1055

• 1155

An iron rod of dia 1 cm and length 8 cm is drawn into a wire of length 18m of uniform thickness. Find the thickness of the wire?

• 0.09cm

• 0.08cm

• 0.06cm

• 0.05cm

Ram has a semicircular disc. He rotates it about its dia by 360°. When he rotates the disc a volume of air in his room gets swept. What is the name of the object / shape that exactly occupies this volume?

• Cylinder

• Hemisphere

• Sphere

• Cuboid