Question

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon.

Estimate the diameter of the Moon, given that the Earth-Moon distance is 3.8 × 105 km. Assume that the pencil has a diameter of about 0.7 cm, and it just blocks out the Moon if it is held about 0.75 m from the eye.

Express your answer using two significant figures.

Answer 1

Answer:

$D = 3.55 \times 10^6 m$

Explanation:

Light rays coming from moon is blocked by the pencil

so as per figure we know that angle subtended by pencil and angle subtended by moon must be same

so we have

$Angle = \frac{Arc}{Radius}$

so we have

$\frac{D}{3.8 \times 10^8 m} = \frac{0.7 cm}{75 cm}$

so we have

$D = 3.55 \times 10^6 m$