68 free MCQs on Circles & Mensuration, each with its own worked answer and explanation. Perimeters, areas, and volumes of 2D and 3D shapes
Take the timed Circles & Mensuration chapterwise test →68 practice questions on Circles & Mensuration, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Circles & Mensuration notes.
Three standard 3D solids and their key formulas: a cylinder's volume scales with the full height, a cone's volume is exactly one-third of the cylinder with the same base and height, and a sphere's volume and surface area both follow distinct r-based formulas worth memorising separately.
Q2.
The diameter of a circle with circumference 44 cm (use π = 22/7):
Q6.
Area of a triangle with base 8 cm and height 5 cm is:
Q7.
The perimeter of a rectangle with length 10 and breadth 6 is:
Q8.
Total surface area of a cylinder (radius r, height h):
Q9.
Volume of a cylinder with radius 3 cm and height 7 cm (π = 22/7):
Q10.
A sector of a circle with radius r and central angle theta (radians) has area:
Q12.
Volume of a cone with base radius r and height h:
Q13.
Curved surface area of a cone with radius r and slant height l:
Q14.
The area of an equilateral triangle with side a is:
Q15.
Length of arc of circle with radius r and central angle θ (radians):
Q16.
A tangent to a circle is:
Q18.
Heron formula for area of triangle with sides a, b, c: A = √[s(s-a)(s-b)(s-c)] where s =
Q19.
The volume of a cuboid (length l, breadth b, height h) is:
Q20.
Area of a trapezoid with parallel sides a and b, height h:
Q21.
The common external tangents to two circles with radii r₁, r₂ and distance d between centres:
Q22.
A circle has chord of length 8 cm. Distance from centre to chord is 3 cm. Radius =
Q23.
Area of sector of radius 7 with angle 60° (π = 22/7):
Q24.
Volume of a frustum (truncated cone) with radii R, r and height h:
Q25.
Area between two concentric circles (radii R and r, R > r):
Q26.
If a hemisphere has radius r, its total surface area is:
Q27.
A sphere is inscribed in a cube of side a. Radius of sphere =
Q28.
Volume of a hollow cylinder (external radius R, internal radius r, height h) is:
Q29.
The angle subtended by a chord at centre is 90°. If chord = 10 cm, radius =
Q31.
Arc length of sector with radius 14 cm and angle 45° (use π = 22/7):
Q32.
The lateral surface area of a pyramid with base perimeter P and slant height l:
Q33.
A circle circumscribes an equilateral triangle of side a. Circumradius R =
Q34.
A solid is formed by rotating a semicircle of radius r about the diameter. Volume =
Q35.
Angle between a tangent and a chord drawn from the point of tangency:
Q36.
Two tangents drawn from an external point to a circle are:
Q38.
The perimeter of a sector with radius 5 and angle 120° (use π ≈ 3.14):
Q39.
Volume of water in a hemispherical bowl of radius 7 cm when half full:
Q40.
The sum of interior angles of a polygon with n sides:
Q41.
The power of a point P with respect to circle (centre O, radius r) is:
Q42.
Ptolemy theorem for a cyclic quadrilateral ABCD states:
Q43.
The angle between two chords intersecting inside a circle equals:
Q44.
Area of circumscribed circle to a triangle with sides a, b, c (using sine rule R = abc/4K):
Q45.
If a sphere is cut by a plane at distance d from centre, the cross-section circle has radius:
Q46.
Isoperimetric inequality states: among all closed curves of fixed perimeter, the one enclosing maximum area is:
Q47.
The radical axis of two non-concentric circles is:
Q48.
For a frustum with top radius r, bottom radius R, height h, slant height l = √(h²+(R-r)²). Lateral SA =
Q49.
Cavalieri principle: two solids have equal volume if:
Q50.
A right circular cone has base radius 6 and slant height 10. Volume =
Q51.
The angle between a tangent to a circle and a secant from the same external point:
Q52.
A sphere of radius R is melted into n small spheres of radius r. Relation:
Q53.
The nine-point circle of a triangle passes through:
Q54.
Surface area of solid cylinder equals that of sphere. If cylinder has height = diameter (h=2r), find ratio of volumes:
Q55.
The area of a regular hexagon with side a:
Q56.
In a circle of radius R, two chords AB and CD intersect at P. Then PA × PB =
Q57.
The equation of a circle with centre at the origin and radius 5 is:
Q58.
The area of a circle of radius 7 cm is (π = 22/7):
Q59.
The centre of the circle x² + y² − 4x − 6y + 9 = 0 is:
Q60.
The circumference of a circle of radius 14 cm is (π = 22/7):
Q61.
The radius of the circle passing through (0, 0), (4, 0) and (0, 6) is:
Q62.
The length of the tangent from (5, 3) to the circle x² + y² − 2x − 4y − 4 = 0 is:
Q63.
The circles x² + y² = 9 and x² + y² − 8x + 7 = 0 are:
Q64.
The shortest distance from the origin to the circle x² + y² − 6x − 8y + 24 = 0 is:
Q65.
The area of the region between two concentric circles of radii 3 and 5 is:
Q66.
A chord of the circle x² + y² = 25 subtends a right angle at the centre. Its length is:
Q67.
The volume of the largest right circular cone that can be inscribed in a sphere of radius 3 is:
Q68.
A sphere and a cube have equal total surface areas. The ratio of the volume of the sphere to that of the cube is:
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