Mensuration MCQ & Answers [PDF Download]
A trapezoid has parallel sides of lengths 18 cm and 32 cm. The perpendicular distance between them is 12 cm. What is the area of the largest circle that can be inscribed in this trapezoid?
A cylindrical tank with radius 3.5 m and height 8 m is filled with water up to 75% of its capacity. If water is being pumped out at a rate of 2 m³ per minute, how long will it take to empty the tank completely?
A cone and a hemisphere have the same base radius of 7 cm. If their total surface areas are equal, what is the height of the cone? (Take π = 22/7)
A rectangular field is 150 m long and 100 m wide. A path of uniform width runs around the inside perimeter of the field. If the area of the path is 1400 m², what is the width of the path?
A metallic sphere of radius 12 cm is melted and recast into a cone with base radius 16 cm. What is the height of the cone?
A regular hexagon is inscribed in a circle of radius 14 cm. What is the area of the region between the circle and the hexagon? (Take π = 22/7)
A hollow cylinder has an external radius of 8 cm, internal radius of 6 cm, and height of 15 cm. If it is melted and recast into a solid cylinder of radius 10 cm, what will be the height of the new cylinder?
A semicircular garden has a diameter of 28 m. A rectangular flower bed of length 16 m and width 8 m is placed inside it. What is the area of the garden that is not occupied by the flower bed? (Take π = 22/7)
A right circular cone has a slant height of 25 cm and a base radius of 15 cm. What is the total surface area of the cone? (Take π = 22/7)
A cuboid has dimensions 12 cm × 9 cm × 8 cm. What is the length of the longest diagonal that can be drawn inside this cuboid?
A square pyramid has a base edge of 16 cm and a slant height of 17 cm. What is the total surface area of the pyramid?
A circular running track has an inner radius of 50 m and an outer radius of 54 m. What is the area of the track? (Take π = 22/7)
A rhombus has diagonals of lengths 24 cm and 18 cm. What is the area of the rhombus and the length of each side?
A rectangular water tank is 8 m long, 6 m wide, and 4 m high. It is filled with water to 3/4 of its height. If 144 identical spherical balls, each with radius 25 cm, are dropped into the tank, by how much will the water level rise?
An equilateral triangle is inscribed in a circle of radius 12 cm. What is the area of the triangle? (Take √3 = 1.732)
A frustum of a cone has radii 8 cm and 5 cm, and a height of 12 cm. What is the volume of the frustum? (Take π = 22/7)
A regular pentagon has a side length of 10 cm. What is the area of the pentagon? (Take sin 36° = 0.588 and cos 36° = 0.809)
A wooden cube of edge 12 cm is painted on all faces and then cut into smaller cubes of edge 3 cm. How many of the smaller cubes will have exactly two faces painted?
A sector of a circle has a central angle of 120° and a radius of 21 cm. What is the area of the sector and the length of its arc? (Take π = 22/7)
A triangular prism has a triangular base with sides 5 cm, 12 cm, and 13 cm. If the height of the prism is 8 cm, what is the total surface area of the prism?
A circular field has a circumference of 264 m. A square is inscribed in this circle. What is the area of the square? (Take π = 22/7)
A hemispherical dome has a radius of 14 m. What is the cost of painting its curved surface at the rate of ₹25 per square meter? (Take π = 22/7)
A rectangular plot of land is 45 m long and 30 m wide. A pathway of uniform width runs around the outside of the plot. If the area of the pathway is 1224 m², what is the width of the pathway?
A solid sphere is cut into two equal hemispheres. If the total surface area increases by 1386 cm², what was the radius of the original sphere? (Take π = 22/7)
A regular octagon is inscribed in a circle of radius 10 cm. What is the area of the octagon? (Take √2 = 1.414)