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### Question 1

What is the length of an edge of a cube if the ratio of volume to the total surface area is 31 : 41?

### Question 2

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) = 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 × 5^{2} = 300 sq. units.

### Question 3

What is the length of a 10 mm wire that has been drawn out of a lump of 33 cu. cm. tin? Take π = 22/7.

### Question 4

What is the weight of a hollow cylindrical pipe 56 cm long, and having internal and external radii as 13 and 15 cm? The pipe is made of a metal of density 9 gm/cc. Take π = 22/7.

### Question 5

When a weight W kg. is kept on a 3 m × 8 m boat floating over a lake, it sinks by 3 cm. What is W, if the density of water is 1000 kg/cu. m?

This Blog Post/Article "Volume and Surface Areas Quiz Set 006" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-02-07. Published on: 2016-05-11