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Surface Areas and Volumes
NCERT Exemplar Ch 11
CBSE_NCERT_EXEMPLAR_CH11
Grade 10

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 $15\text{ cm} \times 10\text{ cm} \times 3.5\text{ cm}$. The radius of each of the depressions is $0.5\text{ cm}$ and the depth is $1.4\text{ cm}$. Find the volume of wood in the entire stand.

Step-by-Step Solution

Key Concept: Volume of wood $= \text{Volume of cuboid} - 4 \times \text{Volume of conical depression}$.
Stepwise Solution:

Volume of cuboid $= 15 \times 10 \times 3.5 = 525\text{ cm}^3$. [1.0 Mark]

Volume of 1 conical depression $= \dfrac{1}{3} \pi r^2 h = \dfrac{1}{3} \times \dfrac{22}{7} \times (0.5)^2 \times 1.4 = \dfrac{1}{3} \times \dfrac{22}{7} \times 0.25 \times 1.4 = \dfrac{1.1}{3} \approx 0.366\text{ cm}^3$. [1.0 Mark]

Volume of 4 depressions $= 4 \times \dfrac{1.1}{3} = \dfrac{4.4}{3} \approx 1.47\text{ cm}^3$.
Volume of wood $= 525 - 1.47 = 523.53\text{ cm}^3$. [1.0 Mark]

Marking Scheme:

• Volume of cuboid $= 525\text{ cm}^3$: 1.0 Mark
• Volume of 4 conical depressions $= 1.47\text{ cm}^3$: 1.0 Mark
• Volume of wood $= 523.53\text{ cm}^3$: 1.0 Mark

Correct Answer:
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