From a wooden cubical block of edge 7cm, the largest possible right conical piece is cut out whose base is - Maths - Surface Areas and Volumes

Question

From a wooden cubical block of edge 7cm, the largest possible right
conical piece is cut out whose base is on one of the face of the
cube Calculate the volume of the cube left in the box and also find
the total surface area of the box left

Manbar Singh · Accepted Answer

We have,Length of each edge of cubical block = a = 7 cmNow, volume of block = a3 = 73 = 343 cm3Now, diameter of the base of cone = edge of cube = 7 cmNow, radius of base of cone, r = diameter2 = 72 = 3
5 cmNow, height of cone , h = 7 cmVolume of cone = 13πr2h = 13×227×72×72×7 = 5396 cm3Now, volume of remaining solid, when conical piece is removed from the block is given byvolume of remaining solid = volume of cubical block - volume of conical piece = 343-5396 = 2058-5396 = 253
17 cm3TSA of remaining solid = TSA of block - base area of cone + CSA of cone =6a2 - πr2 + πrl         l = slant height of cone=6a2 - πr2 + πrr2 + h2=672 - 227×72×72 + 227×723
52+72=294-38 5+11×61 25=294-38 5+11×7 83=294-38 5+86
13=341 63 cm2

From a wooden cubical block of edge 7cm, the largest possible right conical piece is cut out whose base is on one of the face of the cube. Calculate the volume of the cube left in the box and also find the total surface area of the box left.