If the ratio of length, breadth and height of a cuboidal box is 3: 2: I and its volume is 384 cc. then let us calculate the total surface area of the box.
Answers
EXPLANATION.
Ratio of length, breadth and height of a cuboidal box = 3 : 2 : 1.
volume of a cuboidal = 384.
As we know that,
Volume of cuboid = L X B X H.
Let, length = 3x.
Breadth = 2x.
Height = x.
⇒ (3x) X (2x) X (x) = 384.
⇒ 6x³ = 384.
⇒ x³ = 384/6.
⇒ x³ = 64.
⇒ x³ = 4 X 4 X 4.
⇒ x = 4cm.
Length = 3x = 3(4) = 12cm.
Breadth = 2x = 2(4) = 8cm.
Height = x = 4cm.
Total surface area of cuboid.
⇒ 2(lb + bh + hl).
Put the value in the equation, we get.
⇒ 2[(12)(8) + (8)(4) + (4)(12)].
⇒ 2[96 + 32 + 48].
⇒ 2[176].
⇒ 352sq. cm.
Given,
- The ratio of length, breadth and height of a cuboidal box is 3: 2: I
- The Volume of This Cuboid = 384 cubic units
To Find,
- The Total Surface area of Cuboid
Solution,
Let's
The Length = 3X
The Breadth = 2X
The Height = X
The Volume of Cuboid
= 384 cubic units •••( Given )
Length×Breadth×Height = 384 cubic units
3X × 2X × X = 384 cubic units
6X^3 = 384 cubic units
X^3 = 64 cubic units
X = 4 units
The Length = 3 × 4 units = 12 units
The Breadth = 2 × 4 units = 8 units
The Height = 1 × 4 units = 4 units
TSA = 2 ( LB+BH+HL )
TSA = 2 ( 12× 8+8× 4+4× 12 ) Square units
TSA = 2 ( 96+ 32+48 ) Square units
TSA = 2 ( 176 ) Square units
TSA = 352 Square units
Required Answer,
Total Surface area of Cuboid = 352 Square units