The ratio of length, breadth and height of a rectangular solid is 3 : 2 : 1 and its total surface area is 352 sq. cm, then find the length.
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Answer:
length = 12 cm
Step-by-step explanation:
The ratio of length, breadth and height of a rectangular solid is 3 : 2 : 1 and its total surface area is 352 cm².
length = 3a cm, breadth = 2a cm and height = 1a cm
Total surface area of cuboid/rectangle = 2(lb + bh + hl)
Substitute the values,
→ 2(3*2 a² + 2*1 a² + 1*3 a²) = 352
→ 2(6 a² + 2 a² + 3 a²) = 352
→ 2(11 a²) = 352
→ 22a² = 352
→ a² = 16
→ a = 4
Hence, the length of the cuboid is 3(4) = 12 cm, breadth is 2(4) = 8 cm and height is 1(4) = 4 cm.
Therefore, the length is 12 cm.
Answer:
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Let the ratio be in x.
∴ length = 3x
breadth = 2x
and height = x
Given, volume = 384 cc
⇒ 3x × 2x × x = 384
⇒ 6x3 = 384
⇒ x3 =

= 64
⇒ x =

cm.
⇒ x = 4 cm
So, length = 3×4 = 12 cm
breadth = 2×4 = 8 cm
height = 4 cm
Therefore, Surface area of cuboidal box = 2(length× breadth + breadth×height + height×length)
surface area = 2(12×8 + 8×4 + 4×12)
= 2(96 + 32 + 48)
= 2×176
= 352 sq. cm.