The total surface area of a square based prism is 96
2
cm . what is the height of the
prism if the base is 4.0 cm × 4.0 cm?
a 2 cm
b 3 cm
c 4 cm
d 5 cm

Option C

ANSWER:

The height of the prism is 4 cm, so option C is correct.

SOLUTION:

Given, the total surface area of a square based prism is 96 cm2.  

The base is 4.0 cm × 4.0 cm.

Let, the height of the prism be h.

We know that, square based prism will have two square faces and four rectangular faces.

Two square faces will have same dimensions and four rectangular faces will have same area.

Here those dimensions are 4cm and 4cm.

So, area of a square face = 4 x 4

= 16

Now, area of one rectangular face = height x width

= h x 4

= 4h

Now, we know that total surface area  = 96

2 x square area + 4 x area of rectangular face = 96

2 x 16 + 4 x 4h = 96

32 + 16h = 96

16(2 + h) = 96

2 + h = 6

h = 4.

Hence, the height of the prism is 4 cm, so third option is correct.

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