Question 1 :
It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per $m^2$ , find radius of the base.
Question 2 :
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
Question 3 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Lateral surface area of cuboid = 2 h (l + b)
Question 4 :
Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.
Question 5 :
State true or false: Cone having height = h, radius = r and slant height = l, should have the curved surface area of $\pi rl$.
Question 6 :
The lateral surface area of a cube is 256 $m^2$. Find the volume of the cube.
Question 7 :
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$ .Assume $\pi$ =$\frac{22}{7}$.
Question 9 :
Figures that can be drawn easily on our notebooks or cardboards are called ________
Question 10 :
The height of a cone is 16 cm and its base radius is 12 cm. Find the curved surface area of the cone (Use $\pi$ = 3.14).
Question 11 :
Monica has a piece of canvas whose area is 551 $m^2$ . She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 $m^2$ , find the volume of the tent that can be made with it.
Question 12 :
A godown measures 40 m × 25 m × 15 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.
Question 13 :
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Question 14 :
A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent.
Question 15 :
Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.
Question 16 :
A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume.
Question 17 :
If the volume of a right circular cone of height 9 cm is 48 $\pi$ $cm^3$ , find the diameter of its base.
Question 18 :
A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
Question 19 :
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Question 20 :
State true or false: Cylinder whose radius = r, height = h, it's total surface area should be $2\pi rh$.
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d238f59b460d7261f569.jpeg' />
In the above image, a child playing with building blocks, which are of the shape of cubes, has built a structure as shown. If the edge of each cube is 3 cm, find the volume of the structure built by the child.
Question 22 :
State true or false. An edge of a cube measures r cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in $cm^3$) is $(\frac{1}{6})\pi r^3$.
Question 23 :
A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, find how many litres of milk is needed to serve 1600 students
Question 24 :
Find the volume of the right circular cone with radius 6 cm, height 7 cm.
Question 25 :
The volume of a right circular cone is 9856 $cm^3$ . If the diameter of the base is 28 cm, find slant height of the cone .
Question 26 :
A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in $mm^3$ ) is needed to fill this capsule?
Question 27 :
The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
Question 28 :
State true or false: A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d236f59b460d7261f566.jpeg' />
In the above image, Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius? You may take $\pi$=$\frac{22}{7}$ .
Question 30 :
Find the total surface area of a hemisphere of radius 10 cm. (Use $\pi$ = 3.14)
Question 31 :
Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm .
Question 32 :
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 $cm^3$ of wood has a mass of 0.6 g.
Question 33 :
State true or false: Sphere whose radius = r, the surface area must be $4\pi r^{2}$.
Question 34 :
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood .
Question 35 :
State true or false: If the edge of the cube is a, then volume of cube = $a^{3}$
Question 36 :
Find the capacity in litres of a conical vessel with height 12 cm, slant height 13 cm.
Question 37 :
State true or false: A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.
Question 38 :
A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube ?
Question 39 :
The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 $m^2$.
Question 40 :
A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23af59b460d7261f56c.jpeg' />
In the above image, a metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find its inner curved surface area.Assume $\pi$ =$\frac{22}{7}$.
Question 42 :
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Which box has the smaller total surface area and by how much?
Question 43 :
State true or false: If the edge of the cube is a, then Lateral Surface area of cube = $4a^{2}$
Question 44 :
Find the number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit which is 16 m long, 12m wide and 4 m deep.
Question 45 :
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.Assume $\pi$ =$\frac{22}{7}$.
Question 46 :
Find the surface area of a sphere of radius 10.5 cm.
Question 47 :
A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 4989.60. If the cost of white-washing is Rs 20 per square metre, find the inside surface area of the dome.
Question 48 :
A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be required?
Question 49 :
Find the surface area of a sphere of radius 14 cm.
Question 50 :
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the graphite .
