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Home » 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.).
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.).
CBSE | Class 10 | Exercise 13.2 | Maths | NCERT | Surface Areas And Volumes
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.).
Ncert solutions class 10 chapter 13-15

Volume of cuboid = length x width x tallness

We know the cuboid’s measurements as 15 cmx10 cmx3.5 cm

Along these lines, the volume of the cuboid

    \[=\text{ }15\times10\times3.5\text{ }=\text{ }525\text{ }cm^3\]

Here, sorrows resemble cones and we know,

    \[Volume\text{ }of\text{ }cone\text{ }=\text{ }\left( \frac{1}{3} \right)\pi r^2h\]

Given, range (r) = 0.5 cm and profundity (h) = 1.4 cm

    \[\therefore Volume\text{ }of\text{ }4\text{ }cones\text{ }=\text{ }4\times\left( \frac{1}{3} \right)\pi r^2h\]

    \[=\text{ }1.46\text{ }cm^2\]

Presently, volume of wood = Volume of cuboid – 4 x volume of cone

    \[=\text{ }525-1.46\text{ }=\text{ }523.54\text{ }cm^2\]

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