Mensuration
- The diagonals of a rhombus are 16 cm and 12 cm long. What is its perimeter? Answer: B. 40 cm Answer: (B) 40 cm The diagonals of a rhombus bisect each other at right angles, so each side = √(8² + 6²) = 10 cm. Perimete... 1
- A solid metallic sphere of radius 6 cm is melted and recast into a cone whose base radius is 6 cm. What is the height of the cone? Answer: C. 24 cm Answer: (C) 24 cm Volumes are equal: 4/3π (6)³ = 1/3π (6)² h ⇒ h = 4 × 216/36 = 24 cm. 1
- Find the total surface area of a closed cylinder of radius 14 cm and height 6 cm. (Take \(\pi = \frac{22}{7}\).) Answer: A. 1760 cm ² Answer: (A) 1760 cm ² TSA = 2π r(r + h) = 2 × 22/7 × 14 × 20 = 88 × 20 = 1760 cm ² . (528 is only the curved surface ar... 1
- What is the volume of a cylinder with radius 7 cm and height 10 cm (in cubic cm)? (Take \( \pi = \frac{22}{7} \).) Answer: D. 1540 Answer: (D) 1540 V = π r² h = 22/7 × 49 × 10 = 1540 cubic cm. 1
- The perimeter of a rectangle is 64 cm and its length is 6 cm more than its breadth. What is its area (in sq cm)? Answer: C. 247 Answer: (C) 247 l + b = 32 and l − b = 6, so l = 19 cm, b = 13 cm. Area = 19 × 13 = 247 sq cm. 1
- The area of a square is 196 m². What is its perimeter? Answer: C. 56 m Answer: (C) 56 m Side = √196 = 14 m. Perimeter = 4 × 14 = 56 m. 1
- What is the area of a circle of radius 14 cm? Take \(\pi = \frac{22}{7}\). Answer: C. 616 cm² Answer: (C) 616 cm² Area = πr² = 22/7 × 14 × 14 = 616 cm². Trap: 88 cm is the circumference. 1
- What is the area of a triangle with base 18 cm and height 12 cm? Answer: C. 108 cm² Answer: (C) 108 cm² Area = 1/2 × 18 × 12 = 108 cm². 1
- What is the volume of a cube of edge 6 cm? Answer: D. 216 cm³ Answer: (D) 216 cm³ Volume = a³ = 6 × 6 × 6 = 216 cm³. 1
- The circumference of a circle is 44 cm. What is its radius? Take \(\pi = \frac{22}{7}\). Answer: A. 7 cm Answer: (A) 7 cm 2πr = 44, so r = 44 × 7/2 × 22 = 7 cm. Trap: 14 cm is the diameter. 1
- What is the total surface area of a cuboid measuring 12 cm × 8 cm × 5 cm? Answer: B. 392 cm² Answer: (B) 392 cm² TSA = 2(lb + bh + hl) = 2(96 + 40 + 60) = 2 × 196 = 392 cm². Trap: 480 is the volume. 1
- The diagonal of a square is \(10\sqrt{2}\) cm. What is its area? Answer: B. 100 cm² Answer: (B) 100 cm² Area of a square = d²/2 = 200/2 = 100 cm². (Side = 10 cm.) 1
- The perimeter of a rectangle is 46 cm and its area is 120 cm². What is the length of its diagonal? Answer: C. 17 cm Answer: (C) 17 cm l + b = 23 and lb = 120, so l = 15, b = 8. Diagonal = √(15² + 8²) = √289 = 17 cm. Shortcut: d² = (l + b)²... 1
- What is the volume of a cylinder with radius 7 cm and height 10 cm? Take \(\pi = \frac{22}{7}\). Answer: D. 1540 cm³ Answer: (D) 1540 cm³ V = πr²h = 22/7 × 49 × 10 = 1540 cm³. 1
- What is the volume of a right circular cone of radius 6 cm and height 8 cm? Answer: B. 96π cm³ Answer: (B) 96π cm³ V = 1/3π r² h = 1/3 × π × 36 × 8 = 96π cm³. Trap: 288π forgets the 1/3 ; 60π is the curved surface ar... 1
- A metal sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm each. How many small spheres are made? Answer: D. 27 Answer: (D) 27 Number = (6/2)³ = 3³ = 27 (the 4/3π cancels). Trap: 9 compares areas instead of volumes. 1
- What is the area of a triangle with sides 13 cm, 14 cm and 15 cm? Answer: D. 84 cm² Answer: (D) 84 cm² s = 13 + 14 + 15/2 = 21. Area = √(21 × 8 × 7 × 6) = √7056 = 84 cm². 1
- The diagonals of a rhombus are 24 cm and 10 cm. What is its perimeter? Answer: D. 52 cm Answer: (D) 52 cm The diagonals bisect each other at right angles. Side = √(12² + 5²) = 13 cm. Perimeter = 4 × 13 = 52 cm.... 1
- A wheel of radius 35 cm covers a distance of 1.1 km. How many revolutions does it make? Take \(\pi = \frac{22}{7}\). Answer: A. 500 Answer: (A) 500 Circumference = 2 × 22/7 × 35 = 220 cm. 1.1 km = 1,10,000 cm. Revolutions = 110000 ÷ 220 = 500. 1
- If the radius of a circle is increased by 20%, by what percent does its area increase? Answer: B. 44% Answer: (B) 44% Area ∝ r². Shortcut: 20 + 20 + 20 × 20/100 = 44%. 1
- A rectangular garden 40 m long and 30 m wide has a path 2 m wide all around it on the outside. What is the area of the path? Answer: C. 296 m² Answer: (C) 296 m² Outer rectangle = 44 m × 34 m = 1496 m². Path = 1496 − 1200 = 296 m². Shortcut: path outside = 2w(l + b... 1
- The total surface area of a cube is 294 cm². What is its volume? Answer: B. 343 cm³ Answer: (B) 343 cm³ 6a² = 294, so a² = 49 and a = 7 cm. Volume = 7³ = 343 cm³. 1
- What is the total surface area of a solid hemisphere of radius 7 cm? Take \(\pi = \frac{22}{7}\). Answer: A. 462 cm² Answer: (A) 462 cm² TSA of a solid hemisphere = curved 2πr² + base πr² = 3πr² = 3 × 22/7 × 49 = 462 cm². Trap: 308 cm² is... 1
- The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes? Answer: D. 20 : 27 Answer: (D) 20 : 27 V ∝ r²h. Ratio = (2² × 5) : (3² × 3) = 20 : 27. 1