Question

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.


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Answer 1

Given :-

• Length (L) = 15cm
• Breath (B)= 10cm
• Height (H) = 3.5cm
• Radius (r) = 0.5cm
• Depth (h) = 1.4cm

To Find :-

• The volume of wood in the entire stand.

Solution :-

As we know that,

• Volume of cuboid = L × B × H

=> Volume of the cuboid = 15 × 10 × 3.5

=> Volume of the cuboid = 525 cm³

___________________

Here, depressions are like cones and we know,

• Volume of cone = (⅓)πr²h

=> Given, radius (r) = 0.5 cm and depth (h) = 1.4 cm

=> ∴ Volume of 4 cones = 4x(⅓)πr²h

=> Volume of 4 cones = 1.46 cm³ .

=> Now, volume of wood = Volume of cuboid - Volume of 4 cones.

=> 525- 1.46 cm³

=> 523.54 cm³ .

Thus, the volume of wood in the entire stand is 523.54 cm³.

Answer 2

volume of wood in stand = volume of cuboib - volume of 4 cones

volume of cuboid

L = 15

B = 10

H = 3.5         (volume of cuboid =lbh)

15 * 10 * 3.5

=525$cm^3$

volume of cone

r = 0.5

h = 1.4           (volume of cone =1/3 $\pi r^2h$)

$\frac{1}{3} * \frac{22}{7} *.5*0.5*1.4$

$\frac{1}{3} *22*0.5*0.5*0.2$

0.367$cm^{3}$

• volume of 4 cones = 4 * volume of 1 cone    

                                     4 * 0.367

                                      = 1.47

now,

        volume of wood in stand = volume of cuboid - volume of 4 cones

                                     = 525 - 1.47

                                        = 523.53$cm^{2}$