Geometry: Mensuration, Trigonometry

A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod. Find the number of balls.

If the ratio of the areas of 2 squares is 2 : 1, then the ratio of the perimeters of the squares is

In triangle ABC, AB = AC and ∠C = 30°. Find the measure of ∠A.

If the ratio of the area of a sector to the area of a circle is 3:5, what is the ratio of the length of the arc of the sector to the circumference of the circle?

A rectangular plot of land has a fence along three of its four sides, the unfenced side and the side opposite the unfenced side have a length that is three times the length of the other two sides. If the area of the plot is 432 square feet, what is the total length of the fence is feet?

The dimensions of a box are 2,3 and 4 meters. the cost of painting the outer sides of the box at the rate of tk. 3 per square meter is ___

The height of a cylinder is four times the radius of the cylinder. If the volume of the cylinder is 256π cm³, what is the radius of the cylinder?

The number of parallellograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is -

The length of the rectangular hall is 5 m more than its breadth. The area of the hall is 750 m². The length of the hall is:

When the diameter of a circle is trebled, the area is multiplied by how many times?

A pole casts a √3 m long shadow on the ground at an elevation 60°, the height of the pole is-

If the radius of a circle is tripled, the circumference is -

The volume of a cuboid with length, breadth and height as 5x, 3x² and 7x⁴ respectively is:

The length of rectangle ABCD is (6/5)^th of its breadth. Its perimeter is 132. What is its area?

The triangular base of a prism is a right triangle of sides a and b = 2a. The height h of the prism is equal to 10 mm and its volume is equal to 40 mm³, what will be the lengths of the sides a and b of the triangle?

A circle can have how many parallel tangents at a single time?

If 3 sides of a triangle are 6 cm, 8 cm, and 10 cm, then the altitude of the triangle, using the largest side as its base, will be -

City B is 5 miles east of city A. City C is 10 miles southeast of city B. Which of the following is the closest to the distance from city A to City C?

If the radius of a right cylinder is tripled and the height is reduced by 40%, then what would the percentage change in volume?

The side of a square is increased by 10%, by what percent will the area be increased?