Question

Anu makes a cuboid of plasticine of sides 15cm, 30cm and 15cm. How many such cuboids will be need to form a cube?

Answer 1

4 cuboids will be need to form a cube

Solution:

Given that,

Anu makes a cuboid of plasticine of sides 15 cm, 30 cm and 15 cm

Thus,

length = 15 cm

Breadth = 30 cm

Height = 15 cm

Find volume of cubiod:

$Volume\ of\ cuboid = length \times breadth \times height\\\\Volume\ of\ cuboid = 15 \times 30 \times 15\\\\Volume\ of\ cuboid = 6750\ cm^3$

Find L.C.M of given dimensions:

Lcm of 15, 30 and 15

List all prime factors for each number

List all prime factors for each number.  

Prime Factorization of 15 is:  3 x 5

Prime Factorization of 30 is:  2 x 3 x 5

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 3 x 5 = 30

Thus, smallest such cube will have a side length  of 30 cm

Find volume of cube:

$Volume\ of\ cube = (side)^2\\\\Volume\ of\ cube = 30^2\\\\Volume\ of\ cube = 27000$

Find the number of cuboids

$Number\ of\ cuboids = \frac{\text{volume of cube}}{\text{volume of cuboid}}\\\\Number\ of\ cuboids = \frac{27000}{6750}\\\\Number\ of\ cuboids = 4$

Thus 4 cuboids will be need to form a cube

Learn more about cuboids

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