# Volume and Surface Areas Quiz Set 015

### Question 1

The areas of three adjacent faces of a cube are 4, 8 and 32. It's volume is?

A

32 cu. units.

B

34 cu. units.

C

30 cu. units.

D

36 cu. units.

Soln.
Ans: a

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.

### Question 2

How many boxes measuring 1 m × 1m × 1 m should be dropped into a water tank 7 m × 8 m so that the water level rises by 1 m?

A

56 .

B

58 .

C

54 .

D

60 .

Soln.
Ans: a

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.

### Question 3

How much water flows per hour through a pipe of radius 14 cm, if water flows at 10 km/h?

A

196 π cu. m.

B

198 π cu. m.

C

194 π cu. m.

D

200 π cu. m.

Soln.
Ans: a

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.

### Question 4

What is the volume of rain water collected in a right cylindrical can of radius 7 cm, if 7 cm rainfall is recorded in the city?

A

343 π cu. cm.

B

345 π cu. cm.

C

341 π cu. cm.

D

347 π cu. cm.

Soln.
Ans: a

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.

### Question 5

A cuboid block of wood 5 × 10 × 5 is horizontally placed on a table. Then another cube of side 5 is placed on this block. How much surface area is exposed to air?

A

300 sq. units.

B

302 sq. units.

C

298 sq. units.

D

304 sq. units.

Soln.
Ans: a

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. 