The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm3; find its dimensions. (Dimensions means : its length, breadth and height). Also find the total surface area of the cuboid.
Answers
Required Answer:
◕ Length of cuboid=10cm
◕ Breadth of cuboid=6cm
◕ Height of cuboid=4cm
◕ Surface Area=248cm²
______________________
Question:
The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 cm3; find its dimensions. (Dimensions means : its length, breadth and height). Also find the total surface area of the cuboid.
______________________
Given:
- Volume of cuboid=240 cm³
- Given Length, breadth, height in ratio=5:3:2
______________________
Let:
Length of cuboid=5x
Breadth of cuboid=3x
Height of cuboid=2x
______________________
We know:
- Volume of cuboid = Length × breadth × height
- .°. Volume of cuboid=5x × 3x × 2x
- Volume of cuboid=30x³
______________________
A/Q
- Volume of cuboid=240 cm³
- 240=30x³
- x³=240÷30
- x³=8
Cubing both side
- x=2✓
______________________
⇝Length of cuboid=5x
⇝Length of cuboid=5×2
⇝Length of cuboid=10cm✔
⇝Breadth of cuboid=3x
⇝Breadth of cuboid=3×2
⇝Breadth of cuboid=6cm✔
⇝Height of cuboid=2x
⇝Height of cuboid=2×2
⇝Height of cuboid=4cm✔
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⇝Surface Area=2(Length×Width + Width ×Heigt +Height×Length)
⇝Surface Area=2(10×6 + 6×4 +4×10)
⇝Surface Area=2(60+24+40)
⇝Surface Area=2×124
⇝Surface Area=248cm²✔
______________________
hope it helps!
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MATHS
The length, breadth and height of a cuboid are in the ratio 5:3:2. If its volume is 35.937 m
3
, find its dimension. Also find the total surface area of the cuboid.
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ANSWER
Let the length, breadth and height of the cuboid be 5x,3x and 2x respectively.
We know that the volume of the cuboid is l×b×h.
It is given that the volume of the cuboid is 35.937 m
3
, therefore,
35.937=5x×3x×2x
⇒30x
3
=35.937
⇒x
3
=
30
35.937
=1.197
⇒x=
3
1.197
⇒x=0.33
Therefore, the length l=5x=5×0.33=1.65, breadth b=3x=3×0.33=0.99 and height h=2x=2×0.33=0.66
Now, the total surface area of cuboid is 2(lb+bh+hl), therefore, the total surface area with length 1.65 m, breadth 0.99 m and height 0.66 m is:
A=2[(1.65×0.99)+(0.99×0.66)+(0.99×1.65)]=2(1.6335+0.6534+1.089)=2×3.3759=6.7518 m
2
Hence, the dimensions of cuboid is 1.65 m, 0.99 m and 0.66 m and the total surface area of cuboid is 6.7518 m
2
.