Clark went to a shop to buy oil. He has a can of dimensions $4 m\times 7 m\times 13 m$. How much oil should he buy if he needs to fill the can exactly up to half?

Given:
Dimension of can $=4 m\times 7 m\times 13 m$

To find:
Amount of oil to fill half can

Calculation:
Volume of can$$\begin{gathered} =length\times breadth\times height \\ =4 m\times 7 m\times 13 m=364 m^3 \end{gathered}$$

Amount of oil needed to fill half can $=\frac{364}{2}=182 m^3$

Therefore, he needs to buy $182 m^3$of oil to fill the can exactly up to half.

Hence, the correct answer is option A.