Annular path around a circular garden – Outer radius 21 + 3.5 m:\nA circular garden has radius 21 m. A path 3.5 m wide surrounds it outside. Find the area of the path (in m²).

Difficulty: Easy

50.05
57.56
52.12
none
None of these

Correct Answer: none

Explanation:

Introduction / Context:
The path forms a ring (annulus). Its area equals π(R^2 − r^2), with R the outer radius and r the garden radius.

Given Data:

r = 21 m; width = 3.5 m ⇒ R = 24.5 m.

Step-by-Step Solution:

R^2 − r^2 = 24.5^2 − 21^2 = 600.25 − 441 = 159.25.Area = π * 159.25; with π = 22/7 ⇒ area = 159.25 * (22/7) = 500.5 m².

Why 'none':
Given choices (≈50–58) are an order of magnitude too small; correct area is 500.5 m², so select 'none'.

Final Answer:
none (Actual value: 500.5 m²)

← Previous Question Next Question→

More Questions from Area

Melted hemisphere forms a cylinder – Given CSA:TSA = 2:3, hemisphere radius 14 cm:\nA solid hemisphere of radius 14 cm is melted and cast into a cylinder. For the cylinder, curved surface area : total surface area = 2 : 3. Find the cylinder’s base radius (in cm).
Centroid segment length – Triangle XYZ with sides 11, 14, 7 cm:\nG is centroid and M is the midpoint of XY. Given XY = 11 cm, YZ = 14 cm, XZ = 7 cm. Find GM (in cm).
Square inscribed in a circle (radius 4 cm) with an external tangent:\nPQRS is a square inscribed in a circle of radius 4 cm (so the circle's diameter equals the square's diagonal). Side PQ is extended beyond Q to meet a point Y. From Y, a tangent is drawn to the circle touching it at point R. Find the exact length (in cm) of segment SY.
Trapezium with intersecting diagonals split ratio 2:9:\nIn a trapezium, one diagonal divides the other in the ratio 2 : 9 at their intersection. If the longer parallel side is 45 cm, find the exact length (in cm) of the other parallel side.
Direct common tangent between two circles:\nThe distance between the centres is 61 cm, and the radii are 35 cm and 24 cm. Find the length (in cm) of a direct common tangent.
Angle-bisector area split inside a triangle:\nTriangle PQR has area 180 cm^2. Point S lies on QR, and PS is the angle bisector of ∠QPR. If PQ : PR = 2 : 3, find the area (in cm^2) of triangle PSR.
Nested mid-point squares inside a square and an inscribed circle:\nABCD is a square. EFGH is formed by joining midpoints of ABCD; LMNO is formed similarly from EFGH. A circle is inscribed in EFGH and has area 38.5 sq cm. Find the area (in sq cm) of square ABCD.
Circle inscribed in a quadrant of radius 7 cm:\nIn quadrant PQR with radius 7 cm, a circle is inscribed touching both radii and the arc. Find the exact area (in sq cm) of the circle.
Length from centroid to midpoint on a median:\nIn triangle PQR, centroid C. Given PQ = 30 cm, QR = 36 cm, PR = 50 cm. If D is the midpoint of QR, find the exact length (in cm) of CD.
Triangle from alternate vertices of a regular hexagon (side 12 cm):\nPQRSTU is a regular hexagon of side 12 cm. Find the exact area (in sq cm) of triangle SQU.

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion