Question

A square rod is manufactured in the ratio of 3 : 4 : 5 having a surface area of 188 square cm then how much volume of raw material is used to manufacture it??

Answer 1

Given:

• Dimensions of square rod are in ratio 3:4:5.
• Surface area is 188 sq. cm.

To find:

• Volume of raw material used to manufacture the rod

Solution:

• Since all dimensions are different the rod is a cuboid.
• Let length  be 3 x. From ratio we get breadth = 4 x and height = 5 x.
• Surface area of cuboid = 2 x ( l b+ l h + b h)
• ∴ 188 = 2 ( 12 x² + 20 x² + 15 x²)
• 94 = 47 x²
• x = ± √2.
• But length cannot be negative. So we consider only positive value.
• ∴ x = √2
• Length = 3 √2 cm ; Breadth = 4√2 cm ; Height = 5√2 cm.  
• Volume of cuboid = l*b*h
• Volume = 3√2 * 4√2 * 5√2
• Volume = 120 √2 cubic cm.

Answer:

Volume of raw material req to manufacture the rod will be 120 √2 cubic cm.