Volume and Surface Area Questions

• The surface area of a sphere is 5544 cm2. Find its diameter (in cm).
• The line segment AB intersects the straight line CD at B; AB will be smallest when ∠ ABD (in degrees) is
• Δ PQR is right angled at Q. If m∠R = 60°, what is the length of PR (in cm), if RQ = 4√3 cm?
• ΔABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is
• A right triangular prism has equilateral triangle as its base. Side of the triangle is 15 cm. Height of the prism is 20√3 cm. What is the volume (in cm3) of the prism?
• The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?
• A sphere of radius 21 cm is cut into 8 identical parts by 3 cuts (1 cut along each axis). What will be the total surface area (in cm2) of each part?
• The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
• An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
• The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
• The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
• The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?
• A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
• A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
• A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
• What part of the volume of a cube is the pyramid whose base is the base of then cube and whose vertex is the center of the cube?
• The surface areas of three faces of a cuboid sharing a vertex are 20, 32 and 40 sq. mts. What is the volume of the cuboid in cub. m?
• The two sides holding the right-angle in a right-angled triangle are 3 cm and 4 cm long. The area of its circumcircle will be in sq.cm:
• The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is
• In a quadrilateral PQRS, l_S= 90°. A circle (o, r) touches the sides PQ, QR, RS and SP at A, B, C and D respectively. If QR= 38 cm, RS = 25 cm and QA = 27 cm, find 'r'.