Question

show that the volume of a cube whose each edge measures 12m is 9 times the volume of a cuboid of dimensions 8m×6m×4m

Answer 1

Volume of the cube = 12 m × 12 m ×12 m

=${1728 \: m}^{3}$

Volume of the cuboid = 8 m × 6 m ×4 m
=${192 \: m}^{3}$

It is given that the volume of the cube is 9 times the volume of the cuboid of dimensions 8 m×6 m×4 m.

Thus,Volume of the cube =9×Volume of the cuboid
=> ${1728 \: m} ^{3}$=$9×{192 \: m}^{3}$
=>${1728 \: m}^{3}$=${1728 \: m}^{3}$

Hence it is proved that the volume of the cube is 9 times the volume of the cuboid of dimensions 8 m× 6 m ×4 m.

Answer 2

It is proved that Volume of cube is equals to 9 times the volume of the cuboid using given dimensions.

Explanation:

Given Data

For cube, Dimension of each edge (a) = 12 m

For cuboid, the dimensions = 8m × 6m ×4m

To prove - Volume of cube =  9  × Volume of a cuboid ------> (1)

Volume of cube = a³ (cubic units)

Volume of cube = (12)³

Volume of cube = 1728 m³  --------> (2)

Volume of cuboid = Length × Width × Height   (cubic units)

Volume of cuboid = 8m × 6m ×4m

Volume of cuboid = 192 m³  -------->(3)

Substitute (2) and (3) in equation (1)

Volume of cube =  9  × Volume of a cuboid

1728 = 9 × 192

1728 = 1728  

Hence it is proved that the volume of a cube whose each edge measures 12 m is 9 times the volume of a cuboid of dimensions 8m×6m×4m

To Learn More ...

1) Find the volume of a cube whose volume is three times the volume of a cuboid of dimensions 15cm x 12cm x 10cm

https://brainly.in/question/1721601

2)A cuboid measures 48 m by 32 m by 24 m and each edge of a cube measures 16 m.Find the ratio of their volume

https://brainly.in/question/7583083