Question

A pen stand made of a wood is in the shape of a cuboid with four conical depression to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The diameter of each of the depression is 1 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Answer 1

Heya !!!


Diameter of each conical depression (D) = 1 cm


Radius of each conical depression (R) = 1/2 cm.


Depth of each conical depression (H) = 1.4 cm.



Volume of the wood in the stand = (Volume of the cuboid ) - (Volume of 4 conical depressions).


=> ( 15 × 10 × 3.5) - ( 4 × 1/3 πR²H )

=> ( 525 ) - ( 4/3 × 22/7 × 1/2 × 1/2 × 1.4)

=> ( 525 - 4.4/3) cm³.


=>( 525 - 1.47 ) cm³.


=> 523.53 cm³.



HOPE IT WILL HELP YOU....... :-)

Answer 2

Given,

The dimensions of the cuboid:

Length (l) = 15 cm

Breadth (b) = 10 cm

Height (h) = 3.5 cm

The dimensions of the cone:

The radius of each depression is 0.5 cm and depth is 1.4 cm.

Height = 1.4 cm

Radius = 0.5 cm

Solution:

Volume of the wood = Volume of cuboid - 4(volume of cone)

Volume of cuboid:

$volume \: of \: cuboid \: = lbh \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 15 \times 10 \times 3.5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 150 \times 3.5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 525 {cm}^{3}$

$volume \: of \: cone \: = \frac{1}{3} \pi \: {r}^{2} h \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \frac{22}{7} \times \frac{5}{10} \times \frac{5}{10} \times \frac{14}{10} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{11}{30}$

$volume \: of \: four \: cones \: = 4 \times \frac{11}{30} = \frac{44}{30}$

$volume \: of \: wood \: = 525 - \frac{44}{30} = 525 - 1.46 = 523.54 {cm}^{3}$

Therefore the volume of wood is 523.54 cubic units.