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 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 13.16)

Solution:

From the above figure, we can see that the conical depressions do not contain wood. Since the dimensions of all 4 conical depressions are the same, their volumes will also be identical.

Volume of wood in the entire pen stand = Volume of the wooden cuboid - 4 × Volume of the conical depression

We will find the volume of the solid by using formulae;

Volume of the cuboid = lbh, where l, b, and h are the length, breadth, and height of the cuboid respectively.

Volume of the cone = 1/3 πr²h₁, where r and h₁ are the radius and height of the cone respectively.

Depth of each conical depression, h₁ = 1.4 cm

Radius of each conical depression, r = 0.5 cm

Dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm

Volume of wood in the entire pen stand = volume of the wooden cuboid - 4 × volume of the conical depression

= l × b × h - 4 × 1/3 πr²h₁

= (15 cm × 10 cm × 3.5 cm) - (4 × 1/3 × 22/7 × 0.5 cm × 0.5 cm × 1.4 cm)

= 525 cm³ - 1.47 cm³

= 523.53 cm³

The volume of wood in the entire stand is 523.53 cm³.

☛ Check: NCERT Solutions Class 10 Maths Chapter 13

Video Solution:

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 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 13.16).

NCERT Solutions Class 10 Maths  Chapter 13 Exercise 13.2 Question 4 

Summary:

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 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. The volume of wood in the entire stand is 523.53 cm³.

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