# What will be the volume of the prism? If

Base of a right prism is a rectangle, the ratio of whose length and breadth is3:2. If the height of the prism is 12 cm and total surface area is 288 sq. cm, the volume of the prism is

1. 290 cm3
2. 286 cm3
3. 291 cm3
4. 288 cm3

Answer: (4) 288 cm cube

Explanation:-

The ratio of length and width of a rectangular prism = 3: 2
Let the length of a rectangular prism = 3 X and breadth = 2 X
And height = 12 cm    (Given in the  question)

Formula :-
The surface area of a rectangular prism =2 (w h + l w + l h)
Where, w = width of the prism, l =  length of a prism  & h = height of a prism.

Then, 2 (2 X x 12 + 3 X x 2 X + 3 X x 12) = 288                       (Given surface area)
2 (24 X + 6 X^2 + 36 X) = 288
6 X^2 + 60 X = 144
6 X^2 + 60 X – 144 = 0
6 X^2 + 72 X – 12 X – 144 = 0
6 X (X + 12) – 12 (X + 12) = 0
(X + 12) (6 X – 12) =
6 X – 12 = 0
6 X = 12
X = 12/6
X = 2 cm

Then, the length of a rectangular prism = 3 X = 3 x 2
= 6 cm
And width = 2 X = 2 x 2
= 4 cm.

Formula :-
The volume of a rectangular prism = l b h
Where, w = width of the prism, l =  length of a prism  & h = height of a prism.

Then, the volume of a rectangular prism = 6 x 4 x 12
= 288 cm cube

Hence, the answer is (4) 288 cm cube.