10 questionswith explanationsfor RAS, Patwari, VDO and other Rajasthan exams
A cuboidal water tank is 2.5 m long, 1.6 m wide and 1.2 m deep. How many litres of water can it hold?
Answer: (4) 4,800 litres
Explanation
Volume = 2.5 × 1.6 × 1.2 = 4.8 m³, and 1 m³ = 1,000 litres, so 4,800 litres.
The total surface area of a cube is 294 cm². What is its volume?
Answer: (4) 343 cm³
Explanation
6a² = 294 gives a² = 49 and a = 7 cm, so volume = 7³ = 343 cm³.
A cylindrical pillar has a diameter of 56 cm and a height of 3.5 m. What is the cost of painting its curved surface at ₹12.50 per m²? (Take π = 22/7)
Answer: (3) ₹77
Explanation
Curved surface = 2πrh = 2 × 22/7 × 0.28 × 3.5 = 6.16 m², and 6.16 × 12.50 = ₹77.
A right circular cone has a base radius of 7 cm and a height of 24 cm. What is its total surface area? (Take π = 22/7)
Answer: (1) 704 cm²
Explanation
Slant height l = √(7² + 24²) = 25 cm; total surface area = πr(l + r) = 22/7 × 7 × 32 = 704 cm².
The surface area of a sphere is 1,386 cm². What is its volume? (Take π = 22/7)
Answer: (3) 4,851 cm³
Explanation
4πr² = 1,386 gives r² = 110.25 and r = 10.5 cm; volume = (4/3) × 22/7 × 10.5³ = 4,851 cm³.
A solid toy is in the form of a right circular cone mounted on a hemisphere of the same radius, 7 cm. The total height of the toy is 31 cm. What is its total surface area? (Take π = 22/7)
Answer: (3) 858 cm²
Explanation
Cone height = 31 − 7 = 24 cm, slant height 25 cm; area = πrl + 2πr² = 550 + 308 = 858 cm² (the joined base is not exposed).
A solid metal sphere of radius 6 cm is melted and drawn into a uniform cylindrical wire of diameter 0.4 cm. What is the length of the wire?
Answer: (1) 72 m
Explanation
(4/3)π × 6³ = π × 0.2² × L gives L = 288/0.04 = 7,200 cm = 72 m.
A solid metal cone of base radius 12 cm and height 24 cm is melted and recast into solid spheres, each of radius 3 cm. How many spheres are formed?
Answer: (2) 32
Explanation
Cone volume = (1/3)π × 144 × 24 = 1,152π; each sphere = (4/3)π × 27 = 36π; 1,152π ÷ 36π = 32.
A right circular cone has a height of 24 cm and a slant height of 25 cm. What is its volume? (Take π = 22/7)
Answer: (3) 1232 cm³
Explanation
Radius = √(25² − 24²) = 7 cm. Volume = 1/3 × 22/7 × 7 × 7 × 24 = 1232 cm³.
A solid metal sphere of radius 3 cm is dropped into a cylindrical vessel of base radius 6 cm partly filled with water, and it is fully submerged. By how much does the water level rise?
Answer: (2) 1 cm
Explanation
Volume of sphere = 4/3 π × 3³ = 36π cm³. Rise = 36π ÷ (π × 6²) = 1 cm.