Geometry PYQ — Page 5

The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²):

In triangle $ABC$, points $D$ and $E$ are on $AB$ and $AC$ respectively such that $DE$ is parallel to $BC$. If $AD = 6$ cm, $DB = 4$ cm, $AE = 9$ cm, then the length of $EC$ (in cm) is:

In a square, lengths of the diagonals are $(4k + 6)$ cm and $(7k − 3)$ cm. The area of the square (in cm²) is:

Which of the following statements are incorrect? (a) Volume of a cone = $\frac{1}{3}\pi r^3 h$ (b) Volume of a cone = $\frac{1}{3}\pi r^2 h$ (c) Volume of a hemisphere = $\frac{2}{3}\pi r^2$ (d) Volume of a hemisphere = $\frac{2}{3}\pi r^3$ (e) Volume of a cylinder = $\frac{1}{3}\pi r^3 h$ Choose the correct answer from the options given below:

The volumes of 3 solid cubes made of metal are 125 cm$^3$, 64 cm$^3$ and 27 cm$^3$ respectively. After melting all the three cubes a solid cube is made. Find the edge of the new cube.

The volume of a sphere of radius r is obtained by multiplying its surface area with:

The surface area (in $m^2$) of a sphere of radius 7 cm is: Use $\pi = \frac{22}{7}$

The sides of a triangle are in the ratio $\frac{1}{3} : \frac{1}{4} : \frac{1}{5}$. If the semi-perimeter of the triangle is 47 cm, then what is the length of the longest side?

The point (-2, 3) lies in which quadrant?

The length of the side of an equilateral triangle is $4\sqrt{3}$ cm. Find its height.

The heights of two right circular cones are in the ratio 1 : 2 and the circumferences of their bases are in the ratio 3 : 4. Find the ratio of their volumes.

The distance between two parallel sides of a trapezium is 15 m and its area is 480 m$^2$. If one of the parallel sides is 20 m long, then length of the other side is:

The curved surface area of a right circular cylinder of height 14 cm is 88 cm$^2$. The diameter of the base of the cylinder is $\left(\text{Use } \pi = \frac{22}{7}\right)$ :

The circumference of a circular field is 396 m and that of the other circular field is 132 m. Find the area (in m$^2$) of the third circular field whose radius is the sum of the radii of the first two fields. Take $\pi = \frac{22}{7}$

The area of four walls of a rectangular hall having length 18 m and height 8 m is 448 m$^2$. What is the breadth of the hall (in m)?

The area of a right-angled triangle with base 3 m and hypotenuse 5 m is :

The area of a circle is numerically equal to its circumference. Find the diameter of the circle.

The area of a circle is 154 cm$^2$. Find the circumference of the circle. (Take $\pi = \frac{22}{7}$)

The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree is :

Radius of the base and height of a cone are 5 cm and 12 cm respectively. Find its slant height.

Match List - I with List - II. | List - I (Shape) | List - II (Area) | |---|---| | (A) Square | (I) $\pi a^2$ | | (B) Triangle | (II) $b \times h$ | | (C) Circle | (III) $a \times a$ | | (D) Parallelogram | (IV) $\frac{1}{2} b \times h$ | Choose the correct answer from the options given below :

In $\triangle ABC$ with AB = 5 cm, BC = 12 cm, AC = 13 cm and $\angle B = 90^\circ$, which of the following is/are not correct? (a) $\tan C = \frac{12}{13}$ (b) $\text{cosec} A = \frac{13}{12}$ (c) $\sin B = \frac{5}{13}$ (d) $\tan A = \frac{12}{15}$ (e) $\cos C = \frac{12}{13}$ Choose the correct answer from the options given below:

In the given figure DE || BC, the value of x is: 

In the figure, ABCDE and AEPQ are a regular pentagon and a square respectively. What is the measure of angle AQB ?