Find the diameter of a cone whose volume and height are 3696 cubic units and 18 units, respectively. (π=22/7)
A birthday cap is in the form of a right circular cone of base radius 6 cm and height 8 cm. Find the area of the paper sheet required to make 15 such caps. (π =3.14)
The areas of a rectangular garden and a square garden are equal. If the length and the breadth of the first garden are 32 m and 8 m, then find the perimeter of the square garden
If the radius of the base of a right circular cylinder is decreased by 27% and its height is increased by 237%, then what is the percentage increase (closest integer) in its volume?
A cuboid has dimensions of length 10 cm, width 5 cm and height 8 cm. A cube with side length 5 cm is cut out from one of the faces of the cuboid. What is the remaining volume of the cuboid?
In ∆LMN, medians MX and NY are perpendicular to each other and intersect at Z. If MX = 20 cm and NY = 30 cm, what is the area of ∆LMN (in cm² )?
The sum of the length, width and depth of a cuboid is 8 cm and its diagonal is 5 cm.
What is its surface area?
A solid metallic hemisphere of radius 5.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height (in cm) of the cylinder?
If the radius of the base of a right circular cylinder is decreased by 30% and its height is increased by 224%, then what is the percentage increase (closest integer) in its volume?
A solid sphere of diameter 6 cm is melted and then cast into cylindrical wire of radius 0.3 cm. Find the length of the wire.
The area of a triangle is 85 cm² and its base is 5 cm. Find the height of the triangle corresponding to this given base.
If the length I of a room is reduced by 10% and breadth b is increased by 10%, then find the positive change in its perimeter.
The base of the right-angled triangle is 3 m greater than its height. If its hypotenuse is 15 m, then find its area.
Five solid cubes, each of volume 216 cm³, are joined end to end in a linear manner only (single row arrangement) to form a cuboid. What is the lateral surface area (in cm²) of the cuboid?
P is any point inside the rectangle ABCD. If PA = 27 cm, PB = 21 cm, PC = 6 cm, then the length PD (in cm) is equal to:
The area of a square is 900 cm². Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm²) of the hexagon?
If the breadth and height of a closed cuboid are, respectively, 25% and 50% of its length of 12 cm, then find the total surface area of this cuboid.
Which of the following is true?
a) Every trapezium is a parallelogram.
b) Every parallelogram is a square.
c) Every rectangle is a square.
d)Every square is a rhombus.
How many cylinders of radius 10 cm and height 20 cm can be filled with water from a cylinder of radius 20 cm and height 100 cm full of water?
The radius and height of a cylinder are in the ratio 2: 1 Find its total surface area if curved surface area is 616 m²
The ratio of the sum of all the interior angles to an exterior angle of a regular polygon is 24: 1. Find the number of sides
of the polygon.
The floor of an office has dimensions 5 mx 3 m. The cost of painting the walls and ceiling is 7,440 at the rate of 60/m². Find the height of the room (in m). (rounded off to one decimal place)
Select the correct option with respect to the following.
Two triangles are similar if:
a) Any two of their sides are equal
b) their corresponding sides are proportional
c) Any two of their angles are equal
d) their corresponding angles are equal
In a parallelogram two adjacent sides are in the ratio 3: 2 and the perimeter is 65 cm. The length of each of the two shorter
sides of this parallelogram is:
A cuboidal room is of length 15 m, breadth 17 m, and height 21 m. Find the cost of painting its walls and ceiling at the
rate of ₹40/m²
If two parallel lines are intersected by a transversal, then which of the options below is necessarily true?
Find the curved surface area of a cylinder whose diameter of base is 14 m and height is 24 m. [Use: [Use π = 22/7]