446 questions asked across 4 exam years, newest first
A prism has an equilateral triangular base with a side length of 4 cm. Its height starts at 5 cm and increases by 1 cm for each subsequent layer, forming 5 layers in total. What is the total volume of the prism? (Use )
Answer: B
A solid cylinder has a radius of 5 cm and a height of 10 cm. A smaller cylindrical hole of radius 3 cm is drilled coaxially through its entire length. What is the approximate volume of the remaining solid?
Answer: C
A solid hemisphere of radius R is melted and recast into n smaller hemispheres of radius r. Find the value of n.
Answer: A
A point P is 13 cm away from the center of a circle. A tangent is drawn from P to the circle, and its length is 12 cm. What is the area of the circle?
Answer: A
The angle between two tangents drawn from an external point to a circle is 60°. What is the angle subtended by the chord connecting their points of contact at the center?
Answer: B
From a point P outside a circle, a tangent PA and a secant PBC are drawn. If PA = 6 cm and BC = 5 cm, what is the length of the segment PB?
Answer: A
Two identical solid hemispheres, each with a radius of 21 cm, are melted and recast into a single sphere. What is the radius of the new sphere formed?
Answer: B
The side of a regular octagon is half the side of a regular quadrilateral (square). If the perimeter of the quadrilateral is 20 cm, what is the perimeter of the octagon?
Answer: B
A decorative column is made in the shape of a regular hexagonal prism. The side length of its base is 10 cm. The column is built from multiple sections, and their heights form an arithmetic progression: the first section is 5 cm tall, and each subsequent section is 2 cm taller than the previous one. If the column has 4 sections in total, what is the total volume of the column?
Answer: B
In a cyclic quadrilateral ABCD, AB is the diameter of the circle. If angle ACD is 40°, what is the measure of angle BAD?
Answer: B
A marble is spherical in shape with a radius of 4 cm. If the marble is placed inside a cube with side length 10 cm, what is the volume of the cube that is not occupied by the marble?
Answer: B
Two hemispheres of radii 2 cm and 4 cm respectively are melted and recast into another hemisphere. What is the approximate total surface area of the newly formed hemisphere?
Answer: A
△ABC has sides AB = 5 cm, BC = 6 cm, AC = 7 cm. △XYZ is congruent to △ABC. What is the perimeter of △XYZ?
Answer: B
From a point outside a circle, two tangents are drawn to the circle. If one of the tangents measures 12 cm, what is the length of the other tangent?
Answer: C
The inner and outer radii of a hollow hemispherical shell are 7 cm and 14 cm respectively. Find the approximate volume of the metal used.
Answer: B
If the side of a regular hexagon is doubled, what happens to its area?
Answer: C
A cylindrical storage container has a base radius of 3 cm. It is designed with sections whose heights form an arithmetic progression, starting from 2 cm for the bottom section and reaching 10 cm for the topmost section, covering a total of 5 sections. What is the total volume of the container? (Use π≈3.14)
Answer: B
In a triangle ABC with area 60 cm², G is the centroid. What is the area of triangle GBC?
Answer: C
In a circle having a radius 10 cm, a chord is 6 cm away from the center. Find the length of the chord.
Answer: A
A hollow metallic sphere has outer radius 10 cm and is melted to make 50 smaller solid spheres of radius 2 cm. What is the inner radius of the original sphere?
Answer: A
The volume of a hemisphere is numerically equal to four times its curved surface area. Find its radius.
Answer: A
What is the minimum number of cuts required to divide a cuboid into 8 equal cuboids?
Answer: B
If the height of a cone is tripled and the radius is halved, how does the volume change?
Answer: B
The area of a triangle ABC is 16 cm². If a similar triangle DEF has sides that are twice the length of 's sides, what is the area of ?
Answer: C
From an outside point P, two tangents, PA and PB, are drawn to a circle. Given that the length of PA is 12 cm, what is the length of PB?
Answer: C
