Mensuration questions with answers are available for students. The problems have been solved in an elaborate manner to make each and every student understand the concept easily. The questions here are based on Class 8 and Class 10 Maths syllabus. The problems have been prepared, as per the latest NCERT guidelines.
Also, read: Mensuration
Areas of Different Shapes
Area of Rectangle = Length x Breadth
Area of Square = Side2
Area of Triangle = ½ Base x Height
Area of Parallelogram = Base x Height
Area of circle = πr2
Perimeter of polygons = Sum of their sides
Circumference of circle = 2πr
Questions on Mensuration with Solutions
1. A circle has a radius of 21 cm. Find its circumference and area. (Use π = 22/7)
Solution: We know,
Circumference of circle = 2πr = 2 x (22/7) x 21 = 2 x 22 x 3 = 132 cm
Area of circle = πr2 = (22/7) x 212 = 22/7 x 21 x 21 = 22 x 3 x 21
Area of circle with radius, 21cm = 1386 cm2
2. If one side of a square is 4 cm, then what will be its area and perimeter?
Length of side of square = 4 cm
Area = side2 = 42 = 4 x 4 = 16 cm2
Perimeter of square = sum of all its sides
Since, all the sides of the square are equal, therefore;
Perimeter = 4+4+4+4 = 16 cm
Area of quadrilateral = ½ d (h1+h2)
Where d is the diagonal of quadrilateral dividing it into two triangles
h1 and h2 are the heights of two triangles falling on the same base (diagonal of quad.)
Area of Rhombus = ½ d1 d2
Where d1 and d2 are diagonals of rhombus
Area of trapezium = ½ h (a+b)
Where a and b are the two parallel sides of trapezium
h is the distance between a and b.
3. Suppose a quadrilateral having a diagonal of length 10 cm, which divides the quadrilateral into two triangles and the heights of triangles with diagonals as the base, are 4 cm and 6 cm. Find the area of the quadrilateral.
Diagonal, d = 10 cm
Height of one triangle, h1 = 4cm
Height of another triangle, h2 = 6cm
Area of quadrilateral = ½ d(h1+h2) = ½ x 10 x (4+6) = 5 x 10 = 50 sq.cm.
4. A rhombus having diagonals of length 10 cm and 16 cm, respectively. Find its area.
Solution: d1 = 10 cm
d2 = 16 cm
Area of rhombus = ½ d1 d2
A = ½ x 10 x 16
A= 80 cm2
5. The area of a trapezium shaped field is 480 m2, the distance between two parallel sides is 15 m and one of the parallel sides is 20 m. Find the other parallel side.
Solution: One of the parallel sides of the trapezium is a = 20 m, let another parallel side be b, height h = 15 m.
The given area of trapezium = 480 m2
We know, by formula;
Area of a trapezium = ½ h (a+b)
480 = ½ (15) (20+b)
20 + b = (480×2)/15
b = 64 – 20 = 44 m
Total Surface Area of Solid Shapes
TSA of Cuboid = 2(lb + bh + hl)
TSA of Cube = 6l2
TSA of Cylinder = 2πr (r + h)
6. The height, length and width of a cuboidal box are 20 cm, 15 cm and 10 cm, respectively. Find its area.
Solution: Total surface area = 2 (20 × 15 + 20 × 10 + 10 × 15)
TSA = 2 ( 300 + 200 + 150) = 1300 cm2
7. If a cube has its side-length equal to 5cm, then its area is?
l = 5 cm
Area = 6l2 = 6 x 5 x5 = 150 sq.cm
8. Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2.
Solution: : Let height of the cylinder = h, radius = r = 7cm
Total surface area = 2πr (h + r)
TSA = 2 x (22/7) x 7 x (7+h) = 968
h = 15 cm
Volume of Cube, Cuboid and Cylinder
V of cube = l3
Volume of cuboid = l × b × h
Volume of cylinder = πr2h
9. Find the height of a cuboid whose volume is 275 cm3 and base area is 25 cm2.
Solution: Volume of cuboid = l × b × h
Base area = l × b = 25 cm2
275 = 25 × h
h = 275/25 = 11 cm
10. A rectangular piece of paper 11 cm × 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.
Solution: Length of the paper will be the perimeter of the base of the cylinder and width will be its height.
Circumference of base of cylinder = 2πr = 11 cm
2 x 22/7 x r = 11 cm
r = 7/4 cm
Volume of cylinder = πr2h = (22/7) x (7/4)2 x 4
= 38.5 cm3