Question

the whole surface of a cuboid is 214cm square , volume is 210cm cube and the area of the base is 42cm square . find its , edge.

Answer 1

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Answer 2

Given :

The whole surface of a cuboid is 214cm square , volume is 210cm cube and the area of the base is 42cm square

To Find:

find its , edge.

Solution:

Area of base = $Length \times Breadth$

We are given that area of the base is 42cm square

So, Length \times Breadth= 42 ----1

Volume of cuboid = $Length \times Breadth \times Height = 42 \times Height$

We are given that volume is 210cm cube

So,$42 \times Height = 210$

Height = $\frac{210}{42}=5 cm$

Whole surface area of cuboid = 2(l+b)h+2lb=2(l+b)(5)+2(42)=10(l+b)+84

We are given that  whole surface of a cuboid is 214cm square

So,10(l+b)+84=214

10(l+b)=214-84

$(l+b)=\frac{214-84}{10}=13$

l+b=13 ----2

Substitute the value of l from 2 in 1

So,(13-b)b=42

$13b-b^2=42\\b^2-13b+42=0\\b^2-7b-6b+42=0\\b(b-7)-6(b-7)=0\\(b-6)(b-7)=0$

So, b = 6,7

Substitute value of b in 2

at b =6

l+6=13

l=7

at b =7

l+7=13

l=6

So, Dimensions of cuboid is$7 \times 6 \times 5$