Everyday Mathematics: Perimeter and Area | Maths Olympiad Class 6 PDF Download

Q1: The length and breadth of a rectangle are in the ratio 5 : 3. If its perimeter is 128 cm, what is its area?
(a) 768 cm²
(b) 960 cm²
(c) 1024 cm²
(d) 1152 cm²

Ans: (B)
Let length = 5x, breadth = 3x.
Perimeter = $2(5x+3x)=16x2(5x\; +\; 3x)\; =\; 16x$
16x = 128 ⇒ x = 8.
Length = 40, Breadth = 24.
Area = 40 × 24 = 960 cm².

Q2: The diameter of a wheel is 70 cm. How many revolutions will it make to cover a distance of 1.1 km?
(a) 450
(b) 500
(c) 550
(d) 600

Ans: (B)
Circumference = πd = $\frac{22}{7}\times 70=220\backslash frac\{22\}\{7\}\; \times \; 70\; =\; 220$cm.
Distance = 1.1 km = 110000 cm.
Revolutions = 110000 ÷ 220 = 500.

Q3: A square field has an area of 9801 m². Find its perimeter.
(a) 392 m
(b) 396 m
(c) 400 m
(d) 404 m

Ans: (B)
Side = √9801 = 99 m.
Perimeter = 4 × 99 = 396 m.

Q4: The area of a rectangle is 864 cm². If its length is 36 cm, find its perimeter.
(a) 84 cm
(b) 90 cm
(c) 120 cm
(d) 100 cm

Ans: (C)
Breadth = 864 ÷ 36 = 24 cm.
Perimeter = 2(36 + 24) = 120 cm.
Correction → Answer is 120 cm

Q5: A rectangular sheet of paper 44 cm long and 18 cm wide is rolled to form a cylinder. What is the volume of the cylinder?
(a) 1100 cm³
(b) 2200 cm³
(c) 2772 cm³
(d) 3168 cm³

Ans: (C)
When rolled, 18 cm becomes height, 44 cm becomes circumference.
Circumference = 44 ⇒ 2πr = 44 ⇒ r = 7.
Volume = πr²h = $\frac{22}{7}\times 72\times 18=2772\backslash frac\{22\}\{7\}\; \times \; 7²\; \times \; 18\; =\; 2772$
Thus, the answer is 2772 cm³.

Q6: The diagonal of a square field is 14√2 m. What is its area?
(a) 192 m²
(b) 196 m²
(c) 200 m²
(d) 210 m²

Ans: (B)
Diagonal = side√2.
So, side = (14√2 ÷ √2) = 14.
Area = 14² = 196 m².

Q7: The perimeter of a semicircular park is 72 m. Find its radius (use π = 22/7).
(a) 14 m
(b) 18 m
(c) 21 m
(d) 24 m

Ans: (A)
Perimeter = πr + 2r = 72.
$\frac{22}{7}r+2r=72\backslash frac\{22\}\{7\}r\; +\; 2r\; =\; 72$722r+2r=72.
$\frac{22}{r}=72\backslash frac\{22r\; +\; 14r\}\{7\}\; =\; 72$722r+14r=72.
36r = 504 ⇒ r = 14.
Correction → Answer is 14 m (Option A).