Question

A cuboidal wooden toy is of dimensions 14 cm × 17 cm × 4 cm. On its top, there are seven cylindrical hollows for bees to fit in. Each cylindrical hollow is of height 3 cm and radius 2 cm.

Based on the above information, answer the following questions.

1. Find the volume of the wood carved out to make one cylindrical hollow.
2. Find the lateral surface area of the cuboid to paint it with green colour.
3. Find the volume of wood in the remaining cuboid after carving out the seven cylindrical hollows.
4. Find the surface area of the top surface of the cuboid to be painted yellow.

Answer 1

i. Volume of wood carved out for one cylindrical hollow

Given: Radius of hollow, \[r = 2\text{ cm}\]

Height of hollow, \[h = 3\text{ cm}\]

Formula: \[V = \pi r^2 h\]

Calculation: \[V = \frac{22}{7} \times 2^2 \times 3 = \frac{264}{7} \approx 37.71\text{ cm}^3\]

ii. Lateral surface area of the cuboid

Given: Dimensions of cuboid: \[l = 14\text{ cm}\], \[b = 17\text{ cm}\], \[h_c = 4\text{ cm}\]

Formula: \[\text{LSA} = 2(l + b)h_c\]

Calculation: \[\text{LSA} = 2(14 + 17) \times 4\]

\[\text{LSA} = 2 \times 31 \times 4 = 248\text{ cm}^2\]

iii. Volume of wood in the remaining cuboid

Calculation: \[\text{Volume of cuboid} = l \times b \times h_c = 14 \times 17 \times 4 = 952\text{ cm}^3\] 

\[\text{Volume of 7 hollows} = 7 \times \frac{264}{7} = 264\text{ cm}^3\] 

\[\text{Remaining Volume} = 952 - 264 = 688\text{ cm}^3\]

iv. Surface area of the top surface to be painted yellow

Formula: \[\text{Area} = (l \times b) - 7 \times (\pi r^2)\]

Calculation: \[\text{Area} = (14 \times 17) - \left(7 \times \frac{22}{7} \times 2^2\right)\] 

\[\text{Area} = 238 - 88 = 150\text{ cm}^2\]