Volume and Surface Areas Quiz Set 015

Let the sides be L, B and H. Then LB = 4, BH = 8 and LH = 32. Multiplying all three of them L²B²H² = (4 × 8 × 32) = 1024 = 32², which gives LBH = 32 = volume of the cuboid.

The volume of water to be displaced is 7 × 8 × 1 cu. m. This should be equal to the volume of the boxes to be dropped. So N × 1 × 1 × 1 = 7 × 8 × 1, which gives N = 7 × 8 = 56.

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is π × ${14 × 14 × 10 × 1000}/{100 × 100}$, which can easily be cancelled to get 196π cu. m.

The height of the can will be filled to 7 cm. The volume of collected water is same as the volume of cylinder with radius 7 cm and height 7 cm., which equals π7² × 7 = 343π cu. cm.

Let the dimensions of the cuboid be L, 2L and L. Its total surface area is 2(L × 2L + 2L × L + L × L) = 10L². When it is placed on the table, the bottom face is hidden, so net visible area is 10L² - 2L² = 8L². When the cubical block of side L is placed on this block its(i.e., cube's) own L² and L² of the cuboidal block is hidden. So it hides 2L². Thus, the net visible is 8L² + 6L² - 2L² = 12L² = 12 × 5² = 300 sq. units.