Mensuration
- Water flows at 5 km/h through a cylindrical pipe of internal radius 7 cm into a rectangular tank 20 m long and 11 m wide. In how many hours will the water level in the tank rise by 1.4 m? Take \(\pi = \frac{22}{7}\). Answer: A. 4 hours Answer: (A) 4 hours Water per hour = πr² × length = 22/7 × 0.07² × 5000 = 77 m³. Volume needed = 20 × 11 × 1.4 = 308 m³.... 1
- The largest possible right circular cone is cut out of a cube of edge 14 cm. What is the volume of the cone? Take \(\pi = \frac{22}{7}\). Answer: A. 7182/3 cm³ Answer: (A) 7182/3 cm³ The largest cone has radius = 7 cm (half the edge) and height = 14 cm. V = 1/3 × 22/7 × 49 × 14... 1
- The curved surface area of a cylinder is 880 cm² and its height is 10 cm. What is its volume? Take \(\pi = \frac{22}{7}\). Answer: A. 6160 cm³ Answer: (A) 6160 cm³ 2πrh = 880 → r = 880 × 7/2 × 22 × 10 = 14 cm. Volume = πr²h = 22/7 × 196 × 10 = 6160 cm³. Shortcut:... 1
- What is the area of the circle inscribed in an equilateral triangle of side 12 cm? Answer: B. 12π cm² Answer: (B) 12π cm² Inradius of an equilateral triangle = a/2√(3) = 12/2√(3) = 2√(3) cm. Area = π (2√(3))² = 12π cm². Tra... 1
- The length of a rectangle is 3 cm more than its breadth. If the length is increased by 2 cm and the breadth is decreased by 1 cm, the area stays the same. What is the area of the rectangle? Answer: C. 40 cm² Answer: (C) 40 cm² Let the breadth be b. Then (b + 5)(b − 1) = b(b + 3). b² + 4b − 5 = b² + 3b, so b = 5 cm and length = 8... 1
- What is the area of an equilateral triangle of side 8 cm? Answer: A. 16√(3) cm² Answer: (A) 16√(3) cm² Area = √(3)/4a² = √(3)/4 × 64 = 16√(3) cm². 1
- Find the surface area of a sphere of radius 21 cm. (Take \(\pi = \frac{22}{7}\).) Answer: B. 5544 cm² Answer: (B) 5544 cm² Surface area = 4π r² = 4 × 22/7 × 441 = 5544 cm². (1386 is π r² ; 38808 is the volume.) 1
- A cuboid of dimensions 12 cm × 8 cm × 6 cm is melted and recast into cubes of side 2 cm. How many cubes are formed? Answer: C. 72 Answer: (C) 72 Volume of cuboid = 12 × 8 × 6 = 576 cm³. Volume of one cube = 8 cm³. Number = 576 ÷ 8 = 72. 1
- Find the curved surface area of a cylinder of radius 7 cm and height 10 cm. (Take \(\pi = \frac{22}{7}\).) Answer: A. 440 cm² Answer: (A) 440 cm² CSA = 2π r h = 2 × 22/7 × 7 × 10 = 440 cm². 1
- A right circular cone has base radius 6 cm and height 8 cm. What is its curved surface area? Answer: B. 60π cm² Answer: (B) 60π cm² Slant height l = √(6² + 8²) = 10 cm. CSA = π r l = π × 6 × 10 = 60π cm². 1