Home > Surface Areas and Volumes > CBSE_NCERT_EXEMPLAR_CH11 > 0107eb2e-9ac0-5ae9-b694-a9fcc1d64c2a
Not the exact question you were looking for?

Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.

Surface Areas and Volumes
NCERT Exemplar Ch 11
CBSE_NCERT_EXEMPLAR_CH11
Grade 10

Question:

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1\text{ cm}$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Step-by-Step Solution

Key Concept: Volume $= \text{Volume of cone} + \text{Volume of hemisphere} = \dfrac{1}{3}\pi r^2 h + \dfrac{2}{3}\pi r^3$.
Stepwise Solution:

Here $r = 1\text{ cm}, h = 1\text{ cm}$. [0.5 Mark]

Volume of cone $= \dfrac{1}{3} \pi (1)^2 (1) = \dfrac{1}{3} \pi\text{ cm}^3$. [0.5 Mark]

Volume of hemisphere $= \dfrac{2}{3} \pi (1)^3 = \dfrac{2}{3} \pi\text{ cm}^3$. [0.5 Mark]

Total volume $= \dfrac{1}{3} \pi + \dfrac{2}{3} \pi = \pi\text{ cm}^3$. [0.5 Mark]

Marking Scheme:

• Writing volume formulas for cone and hemisphere: 1.0 Mark
• Evaluating total volume $= \pi\text{ cm}^3$: 1.0 Mark

Correct Answer:
Mathbee AI Mentor (Free Demo)

Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.

Master Surface Areas and Volumes with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free