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### 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) = 10L^{2}. When it is placed on the table, the bottom face is hidden, so net visible area is 10L^{2} - 2L^{2} = 8L^{2}. When the cubical block of side L is placed on this block its(i.e., cube's) own L^{2} and L^{2} of the cuboidal block is hidden. So it hides 2L^{2}. Thus, the net visible is 8L^{2} + 6L^{2} - 2L^{2} = 12L^{2} = 12 × 6^{2} = 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?

### 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?

### 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 L^{3} = 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 × (2L^{2} + 2L^{2} + L^{2}) = 10 × L^{2} = 10 × 7^{2} = 490 sq. cm.

This Blog Post/Article "Volume and Surface Areas Quiz Set 008" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.