List of top Mathematics Questions on Mensuration asked in UP Board X

By taking out a hemisphere from both the ends of a wooden solid cylinder, an item is formed. If the height of the cylinder is 10 cm and radius of the base is 3.5 cm, find the total surface area of the item.
If the perimeter of a garden of area 800 m$^2$ is 120 m and its length is twice the breadth, then find its length and breadth.
The surface area of a sphere of diameter $\dfrac{1}{2}$ cm will be

Find the total surface area of the given figure where $AB = 3.5 \text{ cm}$ and height of the toy $CD = 5 \text{ cm.}$ 

Rasheed got a spinning top (Lattu) as his birthday present. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm as shown in the figure. Find the area Rasheed has to colour. (Take } $\pi = \dfrac{22}{7}$ 

A juice seller was serving his customers using glasses as shown in the given figure. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of the glass was 10 cm, then find the apparent capacity of the glass and its actual capacity. (Take } $\pi = 3.14$ \textbf{) 

A chord of a circle of radius 15 cm subtends an angle $60^\circ$ at the centre. Find the area of minor and major sectors of the circle. \[ (\pi = 3.14, \ \sqrt{3} = 1.73) \]
The radius of the base of a cylinder is 3.5 cm. If its height is 8.4 cm, then its curved surface area will be
The angle of a sector of a circle of radius 4 cm is $60^\circ$. Its area will be
If a pipe drained the water from a semi-spherical tank filled with water at the rate of $3 \dfrac{4}{7}$ litres per second, how much time will the pipe take to drain half of the water of the tank if the diameter of the tank is 3 m?
The diameter of a solid pipe is 4 cm whose length is 20 cm. Then the volume of the metal used in the pipe will be
Total surface area of a solid hemisphere with radius $r$ will be
Both the ends of a metallic solid cylinder are semi-spherical. Its total height is 19 cm and the diameter of the cylinder is 7 cm. Find the weight of the solid if the weight of \(1 \, \text{cm}^3\) of the metal is \(4.5 \, \text{g}\).
A chord of a circle of radius 15 cm subtends an angle of \(60^\circ\) at the centre of the circle. Find the area of the corresponding minor segment. \((\pi = 3.14, \, \sqrt{3} = 1.73)\)
Find the volume of a copper rod of length 8 cm whose diameter is 1 cm.
Total surface area of a solid hemisphere with radius \(r\) will be
If the diameter of a sphere is \(d\), then its volume will be
A solid is in the shape of a cone which is surmounted on a hemisphere of same base radius. If the curved surfaces of the hemisphere and the cone are equal, find the ratio of radius and height of the cone.
An arc of a circle of radius 21 cm subtends an angle of \( 60^\circ \) at the centre. Find the area of the sector formed by the arc.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.
The radius of the base of a right circular cone is 3.5 cm and height is 12 cm. Find the volume of the cone.
The length of the minute hand of a clock is \( r \) cm. The area of the sector swept by the minute hand in one minute will be:
The whole surface area of a solid hemisphere of diameter \( \dfrac{1}{2} \, \text{cm} \) will be:
A spherical glass vessel has a cylindrical neck 7 cm long and diameter 2 cm, while the diameter of the spherical part is 8.4 cm. Find how much water can be filled in the vessel.
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.