List of top Mathematics Questions on Mensuration asked in CBSE Class X

Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is
Area of sector of a circle with radius \(18 \text{ cm}\) is \(198 \text{ cm}^2\). The measure of central angle is
In a trapezium \(ABCD\), \(AB \parallel DC\) and its diagonals intersect at \(O\). Prove that \[ \frac{OA}{OC} = \frac{OB}{OD} \]
Find length and breadth of a rectangular park whose perimeter is \(100 \, \text{m}\) and area is \(600 \, \text{m}^2\).
The volume of air in a hollow cylinder is 450 cm\(^3\). A cone of same height and radius as that of cylinder is kept inside it. The volume of empty space in the cylinder is
The volume of air in a hollow cylinder is 450 cm
OAB is sector of a circle with centre O and radius 7 cm. If length of arc \( \widehat{AB} = \frac{22}{3} \) cm, then \( \angle AOB \) is equal to

Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is
AB and CD are diameters of a circle with centre O and radius 7 cm. If \(\angle BOD = 30^\circ\), then find the area and perimeter of the shaded region.
Three measuring rods are of lengths \(120 \, \text{cm}, 100 \, \text{cm}\) and \(150 \, \text{cm}\). Find the least length of a fence that can be measured an exact number of times using any of the rods. How many times each rod will be used to measure the length of the fence?

Fermentation tanks are designed in the form of a cylinder mounted on a cone as shown below:

The total height of the tank is 3.3 m and the height of the conical part is 1.2 m. The diameter of the cylindrical as well as the conical part is 1 m. Find the capacity of the tank. If the level of liquid in the tank is 0.7 m from the top, find the surface area of the tank in contact with liquid.

On the day of her examination, Riya sharpened her pencil from both ends as shown below.

The diameter of the cylindrical and conical part of the pencil is 4.2 mm. If the height of each conical part is 2.8 mm and the length of the entire pencil is 105.6 mm, find the total surface area of the pencil.

If the points \(A(6, 1)\), \(B(p, 2)\), \(C(9, 4)\), and \(D(7, q)\) are the vertices of a parallelogram \(ABCD\), then find the values of \(p\) and \(q\). Hence, check whether \(ABCD\) is a rectangle or not.
Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is
If radius of base is 4 cm and slant height of the cone is 6 cm
A hemispherical bowl is packed in a cuboidal box. The bowl just fits in the box. Inner radius of the bowl is 10 cm. Outer radius of the bowl is 10.5 cm.
hemispherical bowl is packed in a cuboidal box

From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid.
Use $\pi = \dfrac{22}{7}, \sqrt{5} = 2.2$

Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.
Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.