a company is designing a new box to hold coffee . they have 3 designs, cuboid A ( 4cm× 6cm× 25cm) ,B( 10cm× 6cm× 10cm) , C ( 2cm× 20cm×15cm) . all 3designs have the same volume of 600cm³. the company want to choose the design with smallest surface area . which box will have the smallest surface area ?
Answers
Given:
Three design of the coffee holder is given with dimensions.
Cuboid A(4cm×6cm×25cm)
Cuboid B(10cm×6cm×10cm)
Cuboid C(2cm×20cm×15cm)
The three cuboid has the same volume 600cm³
To find:
We need to chose the smallest surface area from the given cuboid.
Solution:
Here, we need to use the formula Total Surface area of the cuboid.
Total surface area of cuboid = 2(lb+bh+hl)
Here, l = length
b = breath
h = height
Cuboid A : 4cm × 6cm× 25cm
Length = 6cm ; Breath = 4cm ; Height = 25cm
Now, we will substitute the values in the formula.
Total surface area of cuboid = 2(lb+bh+hl)
= 2 ((6×4)+(4×25)+(25×6))
= 2 (24+100+150)
= 2(274)
= 548cm²
Cuboid B : 10cm × 6cm× 10cm
Length = 10cm ; Breath = 6cm ; Height = 10cm
Now, we will substitute the values in the formula.
Total surface area of cuboid = 2(lb+bh+hl)
= 2 ((10×6)+(6×10)+(10×10))
= 2 (60+60+100)
= 2(220)
= 440cm²
Cuboid C : 2cm × 20cm× 15cm
Length = 2cm ; Breath = 20cm ; Height = 15cm
Now, we will substitute the values in the formula.
Total surface area of cuboid = 2(lb+bh+hl)
= 2 ((2×20)+(20×15)+(15×2))
= 2 (40+300+30)
= 2(370)
= 740cm²
From the values of Cuboid A , Cuboid B and Cuboid C.
We have found out that the value of the Cuboid B is the smallest surface area.
So, the Cuboid B is the Smallest surface area 440cm².