Question

If for a cuboid the total surface area is 288cm^(2) and length of the diagonal is 12cm then find the volume of the cuboid.
(please provide solution)​

Answer 1

$\bold \pink{Qᴜᴇsᴛɪᴏɴ}$

If for a cuboid the total surface area is 288cm^(2) and length of the diagonal is 12cm then find the volume of the cuboid.

$\bold \blue{Aɴsᴡᴇʀ}$

332.55 cm³

$\bold \green{Exᴘʟᴀɴᴀᴛɪᴏɴ}$

Let L, B and H be the length, width and height of the cuboid respectively.

Length of the diagonal = 12 cm.

Assuming the given diagonal as space diagonal,

L²+B²+H² = 12² —-(1)

Total surface area = 288

2(LB+BH+HL)= 288

LB+BH+HL = 144

LB+BH+HL = 12² —-(2)

Comparing eqn (1) and (2),

L²=LH ; B²=BH ; H²=HL

H=L; B=H; H=L

Therefore, L=B=H. The given cuboid is a cube

From eqn (1),

3L²= 144

L²=48

L= B=H= 4√3

Volume = (4√3)³= 332.55

$\bold \red{Hence \: Verified}$

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Answer 2

$\bold \pink{Qᴜᴇsᴛɪᴏɴ}$

If for a cuboid the total surface area is 288cm^(2) and length of the diagonal is 12cm then find the volume of the cuboid.

$\bold \blue{Aɴsᴡᴇʀ}$

332.55 cm³

$\bold \green{Exᴘʟᴀɴᴀᴛɪᴏɴ}$

Let L, B and H be the length, width and height of the cuboid respectively.

Length of the diagonal = 12 cm.

Assuming the given diagonal as space diagonal,

L²+B²+H² = 12² —-(1)

Total surface area = 288

2(LB+BH+HL)= 288

LB+BH+HL = 144

LB+BH+HL = 12² —-(2)

Comparing eqn (1) and (2),

L²=LH ; B²=BH ; H²=HL

H=L; B=H; H=L

Therefore, L=B=H. The given cuboid is a cube

From eqn (1),

3L²= 144

L²=48

L= B=H= 4√3

Volume = (4√3)³= 332.55

$\bold \red{Hence \: Verified}$