Question 1 :
A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recasted into a sphere. Find the radius of the sphere.
Question 2 :
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
Question 3 :
State true or false: In a right circular cone, height, radius and slant height do not always be sides of a right triangle.
Question 4 :
Figures that can be drawn easily on our notebooks or cardboards are called ________
Question 5 :
Find the volume of a sphere whose radius is 0.63 m.
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d237f59b460d7261f568.jpeg' />
In the above image, a hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs 5 per 100 $cm^2$
Question 7 :
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 8 :
If the lateral surface of a cylinder is 94.2 $cm^2$ and its height is 5 cm, then find radius of its base.Use $\pi$=3.14
Question 9 :
The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per $cm^3$ ?
Question 10 :
State true or false: If the edge of the cube is a, then volume of cube = $a^{3}$
Question 11 :
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 .
Question 12 :
The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 $cm^3$ = 1$l$)
Question 13 :
Curved surface area of a cone is 308 $cm^2$ and its slant height is 14 cm. Find radius of the base.
Question 14 :
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per $m^2$ .
Question 15 :
If the lateral surface of a cylinder is 94.2 $cm^2$ and its height is 5 cm, then find its volume. (Use $\pi$ = 3.14)
Question 16 :
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 17 :
The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
Question 18 :
The diameter of a sphere is decreased by $25\%$. By what per cent does its curved surface area decrease?
Question 19 :
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Question 20 :
A cloth having an area of 165 $m^2$ is shaped into the form of a conical tent of radius 5 m. Find the volume of the cone.
Question 21 :
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per $m^2$ is Rs 15000, find the height of the hall. [Hint : Area of the four walls = Lateral surface area.]
Question 22 :
The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. Find the ratio of their volumes.
Question 23 :
A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the curved surface of the solid so formed.
Question 24 :
State true or false: If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
Question 25 :
Find the amount of water displaced by a solid spherical ball of diameter 28 cm.
Question 26 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Volume of cuboid = lbh
Question 27 :
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
Question 28 :
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find the cost of plastering this curved surface at the rate of Rs 40 per $m^2$.Assume $\pi$ =$\frac{22}{7}$
Question 29 :
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Question 30 :
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 31 :
If the triangle ABC with sides 5 cm,12 cm and 13 cm is revolved about the side 5 cm, then find the volume of the solid so obtained.
Question 32 :
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 33 :
Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions $4m\times3m$?
Question 34 :
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the volume of the cone (taking $\pi=\frac{22}{7}$).
Question 35 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23cf59b460d7261f56f.jpeg' />
In the above image, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.Assume $\pi$ =$\frac{22}{7}$.
Question 36 : <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 38 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23df59b460d7261f571.jpeg' />
In the above image, a right circular cylinder just encloses a sphere of radius r. Find curved surface area of the cylinder.
Question 39 :
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 $cm^2$ .
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d234f59b460d7261f564.jpeg' />
In the above image, Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden box covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively how many square sheets of paper of side 40 cm would she require?
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23cf59b460d7261f570.jpeg' />
In the above image, a right circular cylinder just encloses a sphere of radius r. Find surface area of the sphere.
Question 42 :
Find the volume of the right circular cone with radius 3.5 cm, height 12 cm.
Question 43 :
State true or false: If the edge of the cube is a, then Diagonal of cube = $a\sqrt3$
Question 44 :
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 45 :
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.What is the area of the glass?
Question 46 :
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 47 :
In a cylinder, radius is doubled and height is halved, curved surface area will be _________?
Question 48 :
30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find the total surface area.
Question 49 :
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 50 :
State true or false: Curved surface area of hemisphere is $2\pi r^{2}$.
