Two cubes of side 5 cm are placed together. Find volume of cuboid thus obtained
Answers
Question:
Two cubes of side 5 cm are placed together. Find volume of cuboid thus obtained.
Answer:
Volume of obtained cuboid is 250 cm^3 .
Note:
Cube:-
• Volume = (Side)^3
• Total surface area = 6•(Side)^2
• Lateral surface area = 4•(Side)^2
• Diagonal = √3•Side
Cuboid:-
• Volume = L•B•H
• Total surface area = 2•(L•B + B•H + H•L)
• Lateral surface area = 2•H•(L + B)
• Diagonal = √(L^2 + B^2 + H^2)
where;
L is Length
B is Breadth
H is Height
Solution:
We have two identical cubes each of whose side is of 5 cm.
If we place these two cubes together, then it will form a cuboid whose length will be 10 cm , breadth will be 5 cm and height will be 5 cm.
Thus;
L = 10 cm
B = 5 cm
H = 5 cm
(For figure, please refer to the attachment)
Now,
We know that , the volume of a cuboid;
= L•B•H
= (10 cm)•(5 cm)•(5 cm)
= 10•5•5 cm^3
= 250 cm^3
Hence,
Volume of obtained cuboid is 250 cm^3 .
Also,
We know that, the total surface of a cuboid;
= 2•(L•B + B•H + H•L)
= 2•(10•5 + 5•5 + 5•10) cm^2
= 2•(50 + 25 + 50) cm^2
= 2•125 cm^2
= 250 cm^2
Hence,
The total surface of the obtained cuboid is 250 cm^2 .
Also,
We know that, the lateral surface of a cuboid;
= 2•H•(L + B)
= 2• 5•(10 + 5) cm^2
= 2•5•15 cm^2
= 150 cm^2
Hence,
The lateral surface of the obtained cuboid is 150 cm^2 .
Also,
We know that, the diagonal of a cuboid;
= √(L^2 + B^2 + H^2)
= √(10^2 + 5^2 + 5^2) cm
= √(100 + 25 + 25) cm
= √(150) cm
= 5√6 cm
Hence,
The diagonal of the obtained cuboid is 5√6 cm .
Answer:
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