Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15cm by 10cm by 3.5cm . the radius of each of the depressions is 0.5cm and the depth is 1.4 cm. find the volume of wood in the entire stand.

Answer 1

Answer:

The volume of wood in the entire stand  =  523.53  cm³

Step-by-step explanation:

Here, volume of cuboidal wood pen stand  = l * b * h

where, l = length of pen stand = 15 cm

             b = breadth of pen stand = 10 cm

            h  =  height of pen stand =  3.5  cm

 =>  volume of cuboidal wood pen stand  =  15 * 10 * 3.5

                                                            =  525   cm³

volume of a conical depression  =  1/3 * pi * r² * h

                                               =  1/3 * 22/7 * 0.5 * 0.5 * 1.4

                                                =  0.3666   cm³

So, volume of 4 conical depressions  =  4 * 0.3666

                                                       = 1.467   cm³

Hence, the volume of wood in the entire stand  =  (volume of cuboidal wood pen stand  -  volume of 4 conical depressions)

        => the volume of wood in the entire stand  =   525 -  1.467

                                                                          =   523.53  cm³

Answer 2

Answer:

523.53 cm³

Step-by-step explanation:

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15cm by 10cm by 3.5cm . the radius of each of the depressions is 0.5cm and the depth is 1.4 cm. find the volume of wood in the entire stand.

To find the volume of wood in the entire stand we will find total volume of cuboid shape and then minus the wood removed to make four conical depression to hold pens

Volume of whole cuboid = 15 * 10 * 3.5 = 525 cm³

Volume of one conical depression = $\frac{1}{3} \times \pi r^2 \times h$

r = radius = 0.5 cm  h = depth = 1.4 cm

=> Volume of one conical depression =

$=\frac{1}{3}\times \frac{22}{7} \times (0.5)^{2} \times 1.4\\= \frac{1}{3}\times 22 \times (\frac{1}{2})^{2} \times 0.2\\= \frac{1}{3} \times 11 \times 0.1\\=\frac{1.1}{3}$

volume of 4 = 4 * volume of 1

=> Volume of 4 conical depression = $4\times\frac{1.1}{3} = 1.47 cm^3$

Volume of wood = 525 - 1.47 = 523.53 cm³