the Length breadth and height of a cuboid are in ratio 7 ratio 6 ratio 5 if the surface area of the cuboid is 19 26 CM square find its volume
Answers
Step-by-step explanation:
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let l=7x b=6x h=5x
S.A. of cuboid=2[lb+bh+hl]
1926=2[7x × 6x + 6x × 5x + 5x × 7x]
1926=2[42x^2+30x^2+35x^2]
1926=2X107x^2
107x^2=1926/2=963
x^2=963/107=9
x=3
V=21X18X15=5670cm^3
hope this helps.
Or (the other formula)
The volume of cuboid is 5670 cm³
Step-by-step explanation :
Let the length, breath and height of the cuboid be 7x, 6x and 5x respectively.
According to the question ;
Surface area of cuboid = 1926 cm²
⇒ 2 ( lb + bh + hl ) = 1926
⇒ 2 ( 7x * 6x + 6x * 5x + 5x * 7x ) = 1926
⇒ ( 42 x² + 30 x² + 35x² ) = 1926 / 2
⇒ 107 x² = 963
⇒ x² = 963 / 107
⇒ x² = 9
⇒ x = √9
⇒ x = 3
Therefore, the length, breath and height of the cuboid are ;
Length (l) = 7 * 3 = 21 cm.
Breadth (b) = 6 * 3 = 18 cm.
Height (h) = 5 * 3 = 15 cm.
Volume of cuboid = l × b × h
= 21 × 18 × 15
= 5670 cm³