Question

A prism is in form of rectangle.
Its length be breadth are in ratio
3:2 the height of prism is 12 cm
and total surface area is 288 cm? What
is the volume of prism ?​

Answer 1

Answer:

Let the length of base be 3a cm and breadth be 2a cm

Total surface area of prism :

= [Perimeter of base × height] + [2 × Area of base]

= [2 (3a + 2a) × 12 + 2 × 3a × 2a] sq.cm

= (120a + 12a2) sq.cm

According to the question,

120a + 12a2 = 288

⇒ a2 + 10a = 24

⇒ a2 + 10a - 24 = 0

⇒ a2 + 12a - 2a - 24 = 0

⇒ a (a + 12) - 2 (a + 12) = 0

⇒ (a - 2)(a + 12) = 0

⇒ a = 2 because a ≠

-12

∴ Volume of prism :

= Area of base × Height

= (3a × 2a × 12)cu.cm

= 72a2 cu.cm

= (72 × 2 × 2)cu.cm

= 288 cu.cm