List of top Mathematics Questions on Geometry asked in BSE Manipur Class 10

A metallic sphere of radius \(9\) cm is melted and recast to form a cylinder of radius \(3\) cm. Find the curved surface area of the cylinder.

Find the area of the quadrilateral whose vertices are \( (1,1) \), \( (3,4) \), \( (5,-2) \) and \( (4,-7) \) taken in order.

If three consecutive vertices of a parallelogram are \( A(1,-2) \), \( B(3,6) \) and \( C(5,10) \), find its fourth vertex.

Write down the formula to find the area of a triangle whose vertices are \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\).

State and prove Basic Proportionality Theorem.

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Find the area of a circle whose radius is 7 cm.

Prove that the area of a sector of sectorial angle \( \theta \) and radius \( r \) is \( \dfrac{\pi r^2 \theta}{360} \).

Write the full form of SCORES.

How many tangents can be drawn to a circle through a point lying outside the circle?

A point P is at a distance of 13 cm from the centre of a circle. If the radius of the circle is 5 cm, the length of the tangent from P to the circle is

The volume of the hemisphere of radius \(r\) is

Solve graphically:
\[ 2x + 3y = 5 \] \[ 5x - 4y + 22 = 0 \]

Two concentric circles are of radii \(6\) cm and \(10\) cm. The length of a chord of the larger circle which touches the smaller circle is

Length of an arc of a sector of a circle with radius \(r\) and sectorial angle \(\theta\) (measured in degrees) is