A pen stand is made of wood in the shape of cuboid with three conical

1.	A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Answer» Volume of the wood in the pen stand = Volume of cuboid – Total volume of three depressions. Length of the cuboid (l) = 15 cm Breadth of the cuboid (b) = 10 cm Height of the cuboid (h) = 3.5 cm Volume of the cuboid (V) = lbh = 15 × 10 × 3.5 = 525 cm³. Radius of each depression (r) = 0.5 cm Height / depth (h) = 1.4 cm Volume of each depressions V = \(\frac{1}{3}\)πr²h = \(\frac{1}{3}\) × \(\frac{22}{7}\) × 0.5 × 0.5 × 1.4 = \(\frac{7.7}{3\times7}\) = \(\frac{1.1}{3}\) cm³ Total volume of the three depressions = 3 × \(\frac{1.1}{3}\) = 1.1 cm³ ∴ Volume of the wood = 525 – 1.1 = 523.9 cm³

A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Answer»

Volume of the wood in the pen stand = Volume of cuboid – Total volume of three depressions.

Length of the cuboid (l) = 15 cm

Breadth of the cuboid (b) = 10 cm

Height of the cuboid (h) = 3.5 cm

Volume of the cuboid (V) = lbh = 15 × 10 × 3.5 = 525 cm³.

Radius of each depression (r) = 0.5 cm Height / depth (h) = 1.4 cm

Volume of each depressions V = \(\frac{1}{3}\)πr²h

= \(\frac{1}{3}\) × \(\frac{22}{7}\) × 0.5 × 0.5 × 1.4

= \(\frac{7.7}{3\times7}\) = \(\frac{1.1}{3}\) cm³

Total volume of the three depressions = 3 × \(\frac{1.1}{3}\) = 1.1 cm³

∴ Volume of the wood = 525 – 1.1 = 523.9 cm³