A cuboid is 3 cm by 4 cm by 7 cm. Explain whether doubling all of the dimensions would double the surface area?
Answers
Surface area of cuboid
= 2(lh + lb + lh)
= 2(3*4+3*7+4*7)
= 2(12+21+28)
= 2(61)
= 122cm^2
After doubling the dimensions
Surface area of cuboid
= 2(6*8+6*14+8*14)
= 2(48+84+112)
= 2(244)
= 488cm^2
No, area will not double it will became it's 4 times after double.
Answer:
Given:
Dimensions of Cuboid = 3cm, 4cm and 7cm.
To Explain:
If the dimension will be double then the surface area of cuboid will be also double or not.
Step-by-step explanation:
Surface Area Of Cuboid = 2 ( lb + bh + hl )
= 2 ( 3×4 + 4×7 + 7×3 )
= 2 ( 12 + 28 + 21 )
= 2× 61 = 122 cm^2 ----( 1 )
Now, If we double the dimension of cuboid , the surface area also get double or not, let's see,
Surface Area Of Cuboid = 2 ( lb + bh + hl )
= 2 ( 6×8 + 8×14 + 14×6 )
= 2 ( 48 + 112 + 84 )
= 2 × 160 + 84 = 2× 244
= 488 cm^2. ------( 2 )
From equation 1 and 2 it is cleared that if we doubled the dimension of cuboid then the surface area of cuboid will not be doubled