From a rectangular solid 35cmx30cmx22cm, a conical cavity of base radius 14cm and height 22cm is drilled out. Find:
i) the surface area of the remaining solid,
ii) the volume of the remaining solid,
iii) the weight of the material drilled out if it weighs 14gm per cc.
i.) The surface area should be (surface area of the rectangle) - (area of base of cone) + (area of side of cone)
That's because you initially have the entire surface area of the box
In the image you can see that you lose the area of the top piece, but gain the area of the sides.
ii.) (volume of the rectangle) - (volume of the cone)
For similar reasons as listed in part i. Only this time we care about volume, and we're taking an amount away (which is equal to the volume of the cone).
iii.) Once you've found the volume of the cone needed for part ii, all you should have to do is multiply it by 14 and you'll have the weight of removed material in grams.