Geometry revolves around shapes and their characteristics. It can be categorized into two main branches: Plane Geometry, which deals with flat shapes like lines, circles, and triangles—shapes drawable on a piece of paper; and Solid Geometry, which pertains to the geometry of threedimensional space, the type of space we inhabit.
To elaborate, perimeter refers to the boundary that encloses or surrounds a twodimensional shape.
In this type you will be given a cube of “a” cm and will be asked the volume of largest possible sphere which can be chiseled out from it.
Diagonal of the Sphere: a/2 = Radius
Remaining Empty Space of the Cube: a^{3}  πa^{3}/6
In this type you will be given a sphere of radius “A” cm and will be asked the volume of largest cube which can be chiseled out from it.
Here OA= radius of the sphere. So, diameter of the sphere = 2a
Diagonal of the cube = √3x
(If side of the Square is x)
In this type you will be given a Square BDEF when one of its vertices coincide with the vertex of the right angle of the triangle ABC
Side of the Square:
Area of the Square:
In this type you will be asked the area of the largest Square which can be inscribed in a Semicircle of radius “r”
Area of the Square:
In this type you can be asked the area or Side of the largest Square which can be inscribed in a Quadrant of Radius “r”
Side of the Square: r/√2
Area of Square: r^{2}/2
In this type you will be given a Square DEGF when one of its vertices coincide with the hypotenuse of the right angle of the triangle ABC and you can be asked for the side of the square.
Side of the Square:
In this question you will be asked about the side of the largest cube which will be chiseled out of a cone of height ‘h’ cm and radius ‘r’ cm
Side of Cube:
In this you will be asked about the volume of the largest cylinder which can be chiseled out from a right circular cone.
Maximum Volume of the Cylinder:
Q1: Ratan had a hard wooden board out of which he made an equilateral triangle with a side length of 10 cm. Find it’s area?
Ans: The formula to find the area of an equilateral triangle is
= 43.30cm^{2}
Q2: Sam made a circle out of clay find it’s area in terms of pi given the diameter of circle is 18cm?
Ans: Given Diameter = 18 cm
Radius = 9 cm
Area of circle = πr^{2}
Area = π9^{2}
Area= 81πcm^{2}
Q3: The supplement of 90º is?
Ans: Supplementary angles means those angles whose sum is 180.
According to question:
90º + x = 180
= 180 90 = x
= 90º
Q4: Raj bought a mirror for his room with a length of 12 meters and a diagonal of 15 meters, find the width of the rectangle.
Ans: The width of the rectangle is 9 meters.
In a rectangle, the diagonal divides the rectangle into two congruent rightangled triangles. We can use the Pythagorean Theorem to find the width (‘b’) of the rectangle using the length (‘a’) and the diagonal (‘c’):
Q5: Find Volume of a icecream cone whose radius is 6 cm and height 7 cm?
Ans: We know Volume of cone
= 84πcm^{3}
314 videos170 docs185 tests

1. What is the formula for finding the area of a triangle? 
2. How do you calculate the volume of a cube? 
3. What is the formula for finding the perimeter of a rectangle? 
4. How do you find the area of a circle? 
5. What is the formula for calculating the volume of a sphere? 
314 videos170 docs185 tests


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