Question

From a wooden cylinder of height 28cm and diameter 6cm ,two conical cavities are hollowed out. The diameters of the cones are also 6cm and height 10.5cm. Find the volume of the remaining solids.

Answer 1

Answer:

Step-by-step explanation:

Answer is 594 cubic cms

For STEP BY STEP EXPLANATION See attached photos

Answer 2

GIVEN : height of cylinder = 28cm; diameter of cylinder = 6 cm; diameter of cones = 6cm ; height of cones = 10.5 cm

TO FIND :  volume of remaining solid

SOLUTION : As it is given that from a wooden cylinder two cones are hollowed out .

And we have to find the volume of the remaining cylinder that is left out after the hollowing out.

Volume of Remaining cylinder = Volume of cylinder - volume of two cones

Volume of Cylinder = π$r^{2}$h

                                = $\frac{22}{7}$ × 3 ×3 × 28

                                =  792 $cm^{2}$

As in the question diameter is given , so to find radius of the cylinder we will divide it  by 2. so the radius of cylinder will  be 3cm.

So for the radius of cone we will do the same thing as we did in cylinder, so the radius of cones will be 3cm.

Volume of cone = $\frac{1}{3}$π$r^{2}$h

                           = $\frac{1}{3}$×$\frac{22}{7}$× 3 × 3× 10.5

                            = 99 $cm^{2}$

Volume of 2 cones =  2 × 99

                                  = 198 $cm^{2}$

Volume of remaining cylinder = Volume of cylinder - volume of 2 cones

                                                   = 792 - 198 $cm^{2}$

                                                    = 594 $cm^{2}$

Volume of remaining cylinder is 594 $cm^{2}$.