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  • A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm.

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

Answers (1)

Radius of conical depression = 0.5 cm

            Depth = 2.1 cm

            Volume=\frac{1}{3}\pi r^2 h

                        =\frac{1}{3}\times \frac{22}{7} \times (0.5)^2 \times 2.1

                        =0.55cm^3

            \thereforethe volume of 4 cones =4 \times 0.55=2.2cm^3

            Edge of cube = 3

            The volume of cube     =33    (  Because the volume of cube = a3 )        

            Length of cuboid = 10 cm

            Breadth = 5 cm

            Height = 4 cm

        Volume =l \times b \times h

                        =10 \times 5 \times 4=200 cm^3

            Volume of wood = volume of cuboid – volume of cube - volume of 4 cones

            =200 - 2.2 -27 = 170.8 cm3

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