Question

What is the volume of above shape?
(All dimensions are in cm)

• A. $128$ cm${}^3$
• B. $118$ cm${}^3$
• C. $108$ cm${}^3$
• D. $60$ cm${}^3$

Answer 1

The correct option is C $108$ cm${}^3$


Volume of the above shape can be given by two ways:

1. Making the horizontal slice of given shape as depicted in below figure, as per the above shape, after horizontal slicing we got two rectangular prisms, one at top as depicted in below figure and other at bottom as depicted in below figure, now, adding the volumes of these two rectangular prisms (one at top and other at bottom) will give the volume of given shape.
2. Making the vertical slice of given shape as depicted in below figure, As the the above shape, after vertical slicing we got two rectangular prism, one in right as depicted in below figure, and other in left as depicted in below figure, now, adding the volumes of these two rectangular prisms (one at right and other at left) will give the volume of given shape.

Let's find the volume of given shape by first method: Volume of top rectangular prism $=4\times 3\times 4=48$ cm${}^3$

Volume of bottom rectangular prism $=10\times 3\times 2=60$ cm${}^3$

Therefore, Volume of given shape $=48+60=108$ cm${}^3$

(c) is the correct option