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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. 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

Solution:

Given, 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.

The dimension of cuboid are 10 cm, 5 cm and 4 cm.

The radius of each conical depression is 0.5 cm and the depth is 2.1 cm.

The edge of cubical depression is 3 cm.

We have to find the volume of wood in the entire stand.

Volume of cuboid = length × width × height

Given, length = 10 cm

Width = 5 cm

Height = 4 cm

Volume = 10 × 5 × 4

= 200 cm³

Volume of conical depression = (1/3)πr²h

Given, h = 2.1 cm

r = 0.5 cm

Volume = (1/3)(22/7)(0.5)²(2.1)

= 0.55 cm³

Volume of 4 conical depression = 4(0.55)

= 2.2 cm³

Volume of cube = (edge)³

Given, edge = 3 cm

Volume = (3)³

= 27 cm³

Volume of wood = volume of cuboid - volume of cubical depression - volume of 4 conical depression

= 200 - 27 - 2.2

= 170.8 cm³

Therefore, the volume of wood is 170.8 cm³.

✦ Try This: A pen stand made of wood is in the shape of a cuboid with four conical depressions and two cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 14 cm, 8 cm and 7 cm. The radius of each of the conical depressions is 2 cm and the depth is 4 cm. The edge of the cubical depression is 2.6 cm. Find the volume of the wood in the entire stand.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 20

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

Summary:

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. The volume of the wood in the entire stand is 170.8 cm³

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