# 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

- 290 cm
^{3} - 286 cm
^{3} - 291 cm
^{3} - 288 cm
^{3}

**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.