16.  If a metallic cuboid weighs 16 kg, how much would a miniature cuboid of metal weigh, if all dimensions are reduced to one-fourth of the original ?

0.25 kg
0.50 kg
0.75 kg
1 kg

```Answer

Answer: Option  A Explanation:Let the dimensions of the bigger cuboid be x, y and z.
Then, Volume of the bigger cuboid = xyz.
Volume of the miniature cuboid    = (1⁄4x) (1⁄4y) (1⁄4z) = 1⁄64xyz.
Weight of the miniature cuboid     = (1⁄64 * 16) kg = 0.25 kg. ```

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17.  If the areas of the three adjacent faces of a cuboidal box are 120 cm2, 72 cm2 and 60 cm2 respectively, then find the volume of the box.

720 cm3
864 cm3
7200 cm3
(72)2 cm3

```Answer

Answer: Option  A Explanation:Let the length, breadth and height of the box be l, b and h respectively. Then
Volume = lbh = $\sqrt{\mathrm{\left(lbh\right)2}}$ = $\sqrt{\mathrm{lb * bh * lh}}$ = $\sqrt{\mathrm{120 * 72 * 60}}$ = 720 cm3 ```

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18.  If the areas of three adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cu. cm; then the length of the shortest side is :

10 cm
15 cm
20 cm
30 cm

```Answer

Answer: Option  B Explanation:Let lb = 2x, bh = 3x and lh = 4x.
Then, 24x3 = (lbh)2 = 9000.
= x3 = 375 * 9000 .
= x = 150.
h = 9000⁄300 = 30, l = 9000⁄450 = 20 and b = 9000⁄600 = 15.
Hence, shortest side = 15 cm. ```

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19.  In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is :

75 cu. m
750 cu. m
7500 cu. m
75000 cu. m

```Answer

Answer: Option  B Explanation:Area   = (1.5 * 10000) m2 = 15000 m2.
Depth  = 5⁄100m = 1⁄20m.
Volume = (Area * Depth) = (15000 * 1⁄20)m3 = 750 m3. ```

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20.  The area of the base of a rectangle tank is 6500 cm2 and the volume of water contained in it is 2.6 cubic metres. The depth of water in the tank is :

3.5 m
4 m
5 m
6 m

```Answer

Answer: Option  B Explanation:Volume = (2.6 * 100 * 100 * 100) cu. m
Depth = Volume ⁄ Area of the base = (2.6 * 100 * 100 * 100 ⁄ 6500) cm = 400 cm= 4 m. ```

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