Home > Areas Related to Circles > CBSE_NCERT_EXEMPLAR_CH10 > 2a67dd90-47b3-55f3-b192-6b1e194a3ca1
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.

Areas Related to Circles
NCERT Exemplar Ch 10
CBSE_NCERT_EXEMPLAR_CH10
Grade 10

Question:

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^\circ$ to a distance of $16.5\text{ km}$. Find the area of the sea over which the ships are warned. (Use $\pi = 3.14$)

Step-by-Step Solution

Key Concept: Area $= \dfrac{80}{360} \pi (16.5)^2$.
Stepwise Solution:

Area $= \dfrac{80}{360} \times 3.14 \times 16.5 \times 16.5 = \dfrac{2}{9} \times 3.14 \times 272.25$. [1.5 Marks]

$= \dfrac{2}{9} \times 854.865 = \dfrac{1709.73}{9} = 189.97\text{ km}^2$. [1.5 Marks]

Marking Scheme:

• Formula setup with $\theta = 80^\circ, r = 16.5\text{ km}$: 1.5 Marks
• Evaluating area $= 189.97\text{ km}^2$: 1.5 Marks

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 Areas Related to Circles 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