Given below are the Class 9 Maths Worksheets for Surface area and volume
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's
Question 1) A cube and cuboids have the same volume. The dimensions of cuboids are in ratio 1 : 2 : 4. If the difference between the cost of painting the cuboids and cube whole surface area at rate of Rs 5 per m
^{2} is Rs. 80. Find their volumes.
Question 2) A tent is in shape of right circular cylinder up to a height of 3m and a cone above it. The maximum height of tent above ground is 13.5m. Calculate the cost of painting the inner side of tent at rate of Rs. 3/sq m if radius of base is 14m.
Question 3) A school provides milk to students daily in cylindrical glasses of diameter 7cm. If glass is filled with milk up to a height of 12cm, find how many liters of milk is needed to serve 1600 students.
Question 4) Eight metallic spheres, each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere
Question 5) The diameter of a sphere is decreased by 30%. By what percent its surface area decreases?
Question 6) In a cylinder radius is doubled and height is halved then find its curved surface area.
Question 7) A right- angled ABC with sides 3cm, 4cm & 5cm is revolved about fixed side of 4cm. find the volume of solid generated. Also total surface area of solid.
Question 8) If h, s and v are height, curved surface and volume of cone respectively, prove that 3 v h
^{3} + 9v
^{2} =s
^{2}h
^{2}
Question 9) An edge of a cube measure r cm. If the largest possible right circular cone is cut out of this cube, then find the volume of cone?
Question 10) If p. x, y are height, curved surface area and volume of cone respectively, prove that-
3 yp
^{3} – x
^{2}p
^{2} + 9y
^{2} = 0
Question 11) How many planks of dimensions 5m×25cm×10cm can be stored in a pit which is 20 m long, 6m wide and 80 cm deep?
Question 12) The surface area of a sphere of radius 5cm is 5 times the area of the curved surface area of cone of radius 4cm. Find the height and volume of cone. ( = 22/7)
Question 13) A sweet shop has one spherical ladoo of radius 5cm with the same amount of material, how many ladoos of radius 2.5cm can be made?
Question 14) A sphere and right circular cylinder of same radius have equal volumes by what percentage does diameters of cylinder exceeds its height?
Question 15) Curved surface area of an ice cream cone of slate height 12cm is 113.04m
^{2}. Find the base radius and height of cone ( = 3.14)
Question 16) A semi circular sheet of metal of radius 14cm is to be bent to form an open conical cup. Find the capacity of cup?
Question 17) Two solid spheres made of same metal have weight 5920g and 740g respectively. Determine the radius of larger sphere, if the diameter of smaller one is 5cm.
Question 18) Each edge of cube is increased by 50%. Find the percentage increase in surface area of cube.
Question 19) A residential house society is built in 4000 sq m in area. It has an underground thank to collect the rain water the length, breadth and height of which are 50m, 40m and 4m respectively. If it rains at the rate of 2mm per minute for 5 hours, then calculate the depth of water in the tank. What value is depicted in problem?
Question 20) A rectangular tank is 225m x162m at base with what speed should water flow into it through an aperture 60cm x 45cm so that level of water is raised by 20cm in 2.5 hours.
Question 21) The pillars of a temple are cylindrical shaped. If each pillar has a circular base of radius 20cm and height 7m, then find the quantity of concrete mixture used to build 20 such pillars. Also find cost of concrete mixture at the rate of Rs. 200 per m
^{3}. ( =22/7)
Question 22) 50 circular plates, each of radius 7cm and thickness 12cm are placed one above the other to form a solid right circular cylinder. Find the total surface area and volume of the cylinder
Question 23) Three solid sphere of iron whose diameters are 2cm, 12cm and 16cm respectively is melted into a single solid sphere. Find the radius of solid sphere.
Question 24) Coins of same size (say 5 rupee coin) are placed one above the other and cylindrical block is obtained. The volume of this block is 67.76cm
^{3}. Find no. of coins arranged in block, if thickness of each coin is 2mm and radius of each coin is 1.4cm.
Question 25) Metal spheres, each radius 2cm, are packed in a rectangular box of internal dimensions 16cm x 8cm x 8cm. When 16 spheres are packed, the box filled with preservative liquid. Find the volume of liquid.
Question 26) A semi- circular sheet of metal of diameter 14cm is bent to form an open conical container. Find the capacity of container?
Question 27) A 4cm cube is cut into 1cm cubes. Calculate the total surface area of the small cubes. What is the ratio of surface area of small cubes to that of large cube?
Question 28)A cylindrical pipe opened at both the ends is made of iron sheet which is 2cm thick. If the outer diameter is 12cm and its length is 200cm. Find how many cm
^{3} of iron has been used in making the pipe.
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