Question : A cuboid is of dimensions 80 cm × 64 cm × 50 cm How many small cubes with sides 8 cm can be placed in the given cuboid?
Option 1: 480
Option 2: 700
Option 3: 1000
Option 4: 200
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Correct Answer: 480
Solution : Length of cuboid, $l$ = 80 cm Breadth of cuboid, $b$ = 64 cm Height of cuboid, $h$ = 50 cm Side of a cube, $a$ = 8 cm But height, $h$ should be multiple of $a$. Here, Height utilised = 50 – 2 = 48 cm Let $n$ be the number of cubes. The volume of a cuboid = number of cubes × volume of a cube $l×b×h=n × a^3$ $⇒80 × 64 × 48=n × 8 × 8 × 8$ $⇒n=\frac{80 × 64 × 48}{8 × 8 × 8}$ $\therefore n = 480$ Hence, the correct answer is 480.
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Question : How many identical solid cubes, each having sides that are 3 cm long, can be formed by melting a solid cuboid, whose length, breadth and height are 9 cm, 12 cm and 15 cm, respectively?
Option 1: 50
Option 2: 120
Option 3: 60
Option 4: 90
Question : A cuboid whose sides are 8 cm, 27 cm, and 64 cm is melted to form a new cube. What is the respective ratio of the total surface area of the cuboid and cube?
Option 1: 307 : 216
Option 2: 291 : 203
Option 3: 349 : 248
Option 4: 329 : 237
Question : Two cubes each of edge 14 cm are joined to form a single cuboid. What is the volume of the cuboid formed?
Option 1: 5022 cm3
Option 2: 5244 cm3
Option 3: 5666 cm3
Option 4: 5488 cm3
Question : A large solid cube is melted and cast into ' N ' small solid spheres, each of radius 3 cm, and ' N + 2 ' small solid cuboids, each of dimensions 4 cm × 4 cm × 6.5 cm. If the length of each side of the large solid cube is 12 cm, then find the value of 'N'. [Use $\left.\pi=\frac{22}{7}\right]$
Option 1: 8
Option 2: 5
Option 3: 7
Option 4: 6
Question : Dry deciduous forests are found in areas with rainfall between approx____________.
Option 1: 150 cm and 120 cm
Option 2: 100 cm and 70 cm
Option 3: 200 cm and 150 cm
Option 4: 80 cm and 50 cm
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