MathsSurface Area and VolumeSurface areas and volumes – Volume of a Pen stand

Surface areas and volumes – Volume of a Pen stand

Table of Contents

  • Volume of a Pen Stand
  • Summary
  • What’s Next?

In the previous segment, we derived the formula for the volume of a test tube. In this segment, we will find the volume of a pen stand.

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    Find the volume of the pen stand using the given data

    A pen stand is in the shape of a cuboid with four conical depressions to hold pens.

    Pen stand

    Q. Find the volume of a pen stand as shown in the figure below:

    15cm

    10cm

    3.5cm

    1.4 cm

    0.5 cm

    Dimensions of pen stand

    Solution:

    For the cuboid: length (l) = 15 cm, breadth (b) = 10 cm, height (h) = 3.5 cm

    For the conical depression: radius of circular top (r) = 0.5 cm, depth (h) = 1.4 cm

    Volume of the pen stand = Volume of the cuboid – Volume of the conical depressions

    Volume of the cuboid =

    ∴ Volume of the cuboid =

    ∴ Volume of the cuboid =

    Volume of conical depression =

    ∴ Volume of conical depression

    ∴ Volume of conical depression =

    ∴ Volume of conical depression =

    Thus, the volume of the pen stand =

    ∴ the volume of the pen stand =

    ∴ the volume of the pen stand =

    Thus, the volume of wood in the pen stand is 523.54 cubic cms.

    What’s next?

    In the next segment of Class 10 Maths, we will find the surface area and volume of a gulab jamun.

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