# Volume and Surface Areas Quiz Set 008

### Question 1

A cuboid block of wood 6 × 12 × 6 is horizontally placed on a table. Then another cube of side 6 is placed on this block. How much surface area is exposed to air?

A

432 sq. units.

B

434 sq. units.

C

430 sq. units.

D

436 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 × 62 = 432 sq. units.

### Question 2

What is the volume of a right cone whose cross-section is an isosceles triangle with base 16 cm and slant height 10 cm?

A

128 π sq. cm.

B

129 π sq. cm.

C

127 π sq. cm.

D

\$43{2/3}\$ π sq. cm.

Soln.
Ans: a

One of the right triangles of the isosceles triangle has its base = 16/2 = 8. By Pythagorean theorem, the height = \$√{10^2 - 8^2}\$ = \$√{100 - 64}\$ = 6. The radius of the base of the cone r = 8 cm, and height h = 6 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(8^2 × 6)\$ = 128π.

### Question 3

The areas of three adjacent faces of a cube are 3, 4 and 12. It's volume is?

A

12 cu. units.

B

14 cu. units.

C

10 cu. units.

D

16 cu. units.

Soln.
Ans: a

Let the sides be L, B and H. Then LB = 3, BH = 4 and LH = 12. Multiplying all three of them L2B2H2 = (3 × 4 × 12) = 144 = 122, which gives LBH = 12 = volume of the cuboid.

### Question 4

How many boxes measuring 1 m × 1m × 1 m should be dropped into a water tank 2 m × 4 m so that the water level rises by 1 m?

A

8 .

B

10 .

C

6 .

D

12 .

Soln.
Ans: a

The volume of water to be displaced is 2 × 4 × 1 cu. m. This should be equal to the volume of the boxes to be dropped. So N × 1 × 1 × 1 = 2 × 4 × 1, which gives N = 2 × 4 = 8.

### Question 5

What is the surface area of the cuboid obtained by joining two equal cubes of 343 cu. cm volume each?

A

490 sq. cm.

B

492 sq. cm.

C

488 sq. cm.

D

494 sq. cm.

Soln.
Ans: a

Let the side of a cube be L. Then L3 = 343, which gives L = 7. The resulting cuboid has L = L, H = L, and B = 2L. The surface area is 2 × (LB + BH + HL) = 2 × (2L2 + 2L2 + L2) = 10 × L2 = 10 × 72 = 490 sq. cm. 