Surface Area and Volume of Combination of Solids

Three cubes each of volume 216 cm³ are joined end to end to form a cuboid. Find the total surface area and volumeof the resulting cuboid.

• SA = 216 cm²

  V = 216 cm³

• SA = 252 cm²

  V = 216 cm³

• SA = 504 cm²

  V = 648 cm³

• SA = 252 cm²

  V = 648 cm³

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find: (i) the capacity of the vessel

• 1660 cm³

• 1642.67 cm³

• 500 cm³

• 514 cm³

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find: (ii) the inner surface area of the vessel.

• 1024 cm²

• 572 cm²

• 365 cm²

• 1520 cm²

A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs. 25 per metre [Use π = 22/7].

• Rs. 2750

• Rs. 110

• Rs. 2550

• Rs. 3000

The largest possible sphere is carved out from a solid wooden cube of side 7 cm. Find (i) the volume of the sphere

• 1790.67 cm³

• 179.67 cm³

• 356.14 cm³

• 289 cm³

The largest possible sphere is carved out from a solid wooden cube of side 7 cm. Find (ii) the percentage of wood wasted in the process

• 52.38%

• 47%

• 47.62%

• 42.85%

A cylindrical tub of radius 5cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm. And the total height of the solid is 8.5 cm, find the volume of the water left in the tub.

• 154 cm³

• 770 cm³

• 616 cm³

• 308 cm³

A tent is of the shaped of a right circular cylinder up to a height of 3m and then becomes a right circular cone with a maximum
      height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of ₹2 per square metre, if the radius of the base is 14 m.

• Rs. 2048

• Rs. 2068

• Rs. 1034

• Rs. 5620

A well of diameter 2 m is dug 14 m deep. The earth taken out of it is spread evenly all around it to form an embankment of height 40 cm. Find the width of the embankment.

• 3 m

• 2 m

• 7 m

• 5 m

The rain water from a roof of 22m x 20 m drains into a cylindrical vessel having diameter of base 2m. and height 3.5 m. If the vessel is full, find the rainfall in cm.

• 5 cm

• 2.5 cm

• 8 cm

• 4 cm