Test: Mensuration- 4 - UPSC MCQ

Explanation:

Length of the cuboid = 8 cm

Breadth of the cuboid = 6 cm

Height of the cuboid = 3.5 cm

Volume of the cuboid = length × breadth × height

                    = 8 x 6 x 3.5 = 168cm³

Therefore,volume of  the cuboid = 168cm³

Explanation:

Area of  a parallellogram =  Base x Height = 4 x 2.5 = 10 cm²

:Length of  the cuboid = 8 cm

Width of the cuboid = 3 cm

Height of the cuboid = 5 cm

Volume of  a cuboid  = length × breadth × height

Therefore, Volume of the given cuboid = 8x3x5 = 120 cm³

Explanation:Length of the rectangle,l = 4cmBreadth of the rectangle,b = 3 cmPerimeter of a rectangle = 2(l+b) = 2(4+3) = 2x7 = 14 cm

Explanation:Area of a rhombus = Half the product of its diagonals                               = 1/2 x d₁x d₂

Explanation:Area of a trapezium =( Half of the sum of the length of parallel sides )×(perpendicular distance between them)

Explanation:Surface area of a cuboid = 2(lb + bh + hl)where, l= lengthb = breadthand h = height

Explanation:The surface area of a three-dimensional figure is the sum of the areas of all its faces.

Let hypotenuse = x cm
Then, by Pythagoras theorem:
x² = (48020)² + (36015)²
x fi 60025 cm

Let inner radius = A; then 2pr = 440 \ p = 70
Radius of outer circle = 70 + 14 = 84 cm
 Outer diameter = 2 × Radius = 2 × 84 = 168

Volume of soil removed = l × b × h
= 7.5 × 6 × 1.5 = 67.5 m³

Let the common ratio be = x
Then, length = 4x, breadth = 3x and height = 2x
As per question;
2(4x x 3x + 3x x 2x + 2x x 4x) = 8788
2(12x2 + 6x2 + 8x2) = 8788 fi 52x2 = 8788
fi x = 13
Length = 4x = 52 cm

h=volume/area of base
h=1240/40
h=31

Let the radius of the wheel be = p
Then 5000 × 2pr = 1100000 cm fi r = 35 cm

In 4 days, the short hand covers its circumference
4 × 2 = 8 times long hand covers its circumference
4 × 24 = 96 times
Then they will cover a total distance of:-
(2 × p × 4)8 + (2 × p × 6)96 fi 3818.24 cm