The volume of a rectangular parallelopiped is twice the volume of a cube. If the length, breadth and height of the parallelopiped are 9cm, 8cm and 6cm respectively, then find the length of each side of the cube and also its surface area.
Answers
Answer:
Length of each side of the cube = 6 cm
Surface area = 216 cm²
Step-by-step explanation:
Length of the rectangular parallelopiped ( l ) = 9 cm
Breadth of the rectangular parallelopiped ( b ) = 8 cm
Height of the rectangular parallelopied ( h ) = 6 cm
Let the length of each side of the cube be 's* cm
Given :
Volum of the parallelopiped = 2 × Volume of the cube
- Volume of the parallelopiped = lbh cu.units
- Volume of cube = s³ cu. units
⇒ lbh = 2 × s³
⇒ 9 × 8 × 6 = 2 × s³
⇒ 432 = 2s³
⇒ 432 / 2 = s³
⇒ 216 = s³
⇒ s = ³√216
⇒ s = 6
Therefore the length of each side of the cube is 6 cm.
Surface area of cube = 6s² sq. units
= 6 × 6²
= 6³
= 216 cm².
Therefore the surface area of the cube is 216 cm².
AnswEr:-
Length of each side of the cube = 6 cm
Surface area = 216 cm²
Length of the rectangular parallelopiped ( l ) = 9 cm
Breadth of the rectangular parallelopiped ( b ) = 8 cm
Height of the rectangular parallelopied ( h ) = 6 cm
Let the length of each side of the cube be 's* cm
Given :
Volum of the parallelopiped = 2 × Volume of the cube
Volume of the parallelopiped = lbh cu.units
Volume of cube = s³ cu. units
⇒ lbh = 2 × s³
⇒ 9 × 8 × 6 = 2 × s³
⇒ 432 = 2s³
⇒ 432 / 2 = s³
⇒ 216 = s³
⇒ s = ³√216
⇒ s = 6
Therefore the length of each side of the cube is 6 cm.
Surface area of cube = 6s² sq. units
= 6 × 6²
= 6³
= 216 cm².
Therefore the surface area of the cube is 216 cm².
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