Mensuration — Mental Maths

Fill in the blanks:

(i) Area of a parallelogram = base × .....

(ii) Area of a trapezium = $\dfrac{1}{2}$ × ..... × distance between parallel sides

(iii) Area of a rhombus = $\dfrac{1}{2}$ × product of .....

(iv) Area is measured in ..... units.

(v) Volume of a solid is the measurement of ..... occupied by it.

(vi) Volume is measured in ..... units.

(vii) The volume of a unit cube is .....

(viii) 1 litre = ..... cm³

(ix) 1 m³ = ..... litres

(x) Volume of a cuboid = ..... × height.

(xi) Cylinders in which line segment joining the centres of the circular faces is perpendicular to the base are called .....

(xii) Volume of a cylinder = area of base × .....

(xiii) Area of four walls = perimeter of floor × .....

(xiv) Lateral surface area of a cube = 4 × (.....)²

(xv) Total surface area of a cylinder of radius r and height h is .....

Answer

(i) Area of a parallelogram = base × height.

(ii) Area of a trapezium = $\dfrac{1}{2}$ × sum of parallel sides × distance between parallel sides

(iii) Area of a rhombus = $\dfrac{1}{2}$ × product of diagonals.

(iv) Area is measured in square units.

(v) Volume of a solid is the measurement of the space occupied by it.

(vi) Volume is measured in cubic units.

(vii) The volume of a unit cube is 1 cubic unit.

(viii) 1 litre = 1000 cm³

(ix) 1 m³ = 1000 litres

(x) Volume of a cuboid = area of base or length × breadth × height.

(xi) Cylinders in which line segment joining the centres of the circular faces is perpendicular to the base are called right circular cylinders.

(xii) Volume of a cylinder = area of base × height.

(xiii) Area of four walls = perimeter of floor × height of the room.

(xiv) Lateral surface area of a cube = 4 × (side)²

(xv) Total surface area of a cylinder of radius r and height h is 2πr(h + r).

State which of the following statements are true (T) or false (F):

(i) Perimeter of a rectangle is the sum of lengths of its four sides.

(ii) Area of a quadrilateral can be found by splitting it into two triangles.

(iii) Perimeter of a circle of radius r = πr².

(iv) Volume of a cube = 6 × (side)²

(v) 1 m³ = 100000 cm³

(vi) Total surface area of a cuboid = 2(lb + bh + hl)

(vii) There is no difference between volume and capacity.

(viii) Total surface area of a cylinder = lateral surface area + area of two circular ends.

(ix) Surface area of a cube = 4 × (side)²

(x) Lateral surface area of a cuboid = perimeter of base × height

Answer

(i) True

Reason:

The perimeter of a closed figure is the total length of its boundary. So, the perimeter of a rectangle is the sum of the lengths of its four sides.

(ii) True

Reason:

A diagonal of a quadrilateral divides it into two triangles. So, the area of a quadrilateral can be found by adding the areas of these two triangles.

(iii) False

Reason:

The perimeter (circumference) of a circle of radius r is 2πr. The expression πr² gives the area of the circle, not its perimeter.

(iv) False

Reason:

Volume of a cube = (side)³. The expression 6 × (side)² gives the total surface area of the cube.

(v) False

Reason:

1 m = 100 cm, so 1 m³ = 100 × 100 × 100 cm³ = 1000000 cm³.

(vi) True

Reason:

A cuboid has three pairs of identical opposite faces of areas lb, bh and hl. So, its total surface area = 2(lb + bh + hl).

(vii) False

Reason:

Volume is the amount of space occupied by a solid, whereas capacity is the amount of substance that the solid can hold. So, they are not the same.

(viii) True

Reason:

The total surface area of a cylinder is the sum of its lateral (curved) surface area and the areas of its two circular ends, that is, 2πrh + 2πr².

(ix) False

Reason:

A cube has six identical square faces, so its surface area = 6 × (side)². The expression 4 × (side)² gives the lateral surface area of the cube.

(x) True

Reason:

Lateral surface area of a cuboid = 2(l + b)h = perimeter of the base × height.