446 questions asked across 4 exam years, newest first
A circle is inscribed within a right triangle. Considering that the lengths of the two legs measure 6 cm and 8 cm, what is the radius of the inscribed circle?
Answer: A
A spherical ball is submerged in water in a cylindrical container. The radius of the cylindrical container is 5 cm, and the height is 30 cm. What is the volume of water displaced by the ball if its radius is 4 cm?
Answer: D
A hemispherical dome covers a circular area of diameter 20 m. What is the approximate curved surface area of this dome?
Answer: A
A square pyramid has lateral surface area equal to twice the base area. If base side = 6 cm, find slant height.
Answer: A
A triangle ABC is inscribed in a circle. A tangent is drawn to the circle at point A, intersecting the extension of side BC at D. If AD = 6 cm and CD = 4 cm, what is the length of side BC?
Answer: A
A circle with radius x touches another circle with radius 2x externally. What is the length of a direct common tangent?
Answer: C
Two circles with radii 6 cm and 2 cm have their centers 10 cm apart. How many common tangents can be drawn between them, and what type(s) of tangents are they?
Answer: A
Two chords AB and CD intersect at a point P inside a circle. If AP = 6 cm, PB = 8 cm, and CP = 4 cm, what is the length of PD?
Answer: B
A sphere is melted and recast into 8 identical cones, each with radius 3 cm and height 4 cm. What was the radius of the original sphere?
Answer: A
The area of a regular hexagon is made up of how many equilateral triangles?
Answer: D
A tent designed as a triangular prism features a triangular base with an area of 20 m² and a height of 6 m. What is the volume of this tent?
Answer: B
Three non-overlapping, non-touching circles are drawn in a plane. What is the maximum number of distinct common tangents that can be drawn to them in total?
Answer: D
In a circle, chord AB and chord CD intersect at E such that AE : EB = 2 : 3 and CE : ED = 5 : 2. If AB = x and CD = y, which of the following is true?
Answer: D
A chord in a circle with radius 10 cm subtends an angle of 90° at the centre. What is the area of the minor segment?
Answer: A
A sphere is completely contained within a cylinder, with the height and diameter of the cylinder matching the diameter of the sphere. Given that the volume of the sphere is 36π cm³, what is the volume of the vacant space inside the cylinder?
Answer: C
A hemisphere is melted and recast into a cone of the same radius R. Find the height of the cone formed.
Answer: A
Two solid hemispheres of radii 6 cm and 8 cm respectively are melted and recast into a single hemisphere. What is the approximate radius of the new hemisphere formed?
Answer: A
A regular right pyramid has a square base with a side length of 12 cm. Its slant height is 10 cm. What is its volume?
Answer: A
Two circles of radii 9 cm and 5 cm have their centers 17 cm apart. What is the length of the internal common tangent?
Answer: C
Two circles with radii r₁ = 7 cm and r₂ = 3 cm have their centers 20 cm apart. Find the length of the transverse common tangent between them.
Answer: A
A circle is circumscribed about a triangle. If one of the angles of the triangle is 120°, and the radius of the circumscribed circle is r, what is the length of the side opposite the 120° angle?
Answer: A
How many hemispheres with a radius of 3 cm can be produced by melting down a hemisphere with a radius of 12 cm?
Answer: B
A cylinder and hemisphere have the same radius. Their combined height is 30 cm. If the cylinder and hemisphere have equal volumes, find the radius.
Answer: D
A pyramid has a base area of 60 cm² and height 9 cm. What is its volume?
Answer: A
A circular disc of radius 7 cm is inscribed inside an equilateral triangle. What is the approximate area of the remaining portion of the triangle?
Answer: A
