Question 1 :
The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
Question 2 :
Find the surface area of a sphere of radius 14 cm.
Question 3 :
A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. Find the capacity of the cup.
Question 4 :
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In the above image, a right circular cylinder just encloses a sphere of radius r. Find curved surface area of the cylinder.
Question 5 :
Find the volume of a sphere whose surface area is 154 $cm^2$ .
Question 6 :
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 7 :
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 8 :
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
Question 9 :
The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.
Question 10 :
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs 12.50 per $m^2$.Assume $\pi$ =$\frac{22}{7}$.
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 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 13 :
The volume of a right circular cone is 9856 $cm^3$ . If the diameter of the base is 28 cm, find height of the cone.
Question 14 :
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?
Question 15 :
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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 16 :
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 17 :
The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?Assume $\pi$ =$\frac{22}{7}$.
Question 18 :
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 19 :
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. How much of tape is needed for all the 12 edges?
Question 20 :
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In the above image, a wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per $cm^2$ and the rate of painting is 10 paise per $cm^2$ , find the total expenses required for polishing and painting the surface of the bookshelf.
Question 21 :
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet, determine the cost of sheet for it , if a sheet measuring 1 $m^2$ costs Rs 20.
Question 23 :
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 24 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Diagonal of cuboid = $6\sqrt{l^{2}+b^{2}+h^{2}}$.
Question 25 :
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 26 :
A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height ?
Question 27 :
Find the surface area of a sphere of radius 5.6 cm.
Question 28 :
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 29 :
If we cut out many of the plane figures and stack them up in a vertical pile is called ______
Question 30 :
The paint in a certain container is sufficient to paint an area equal to 9.375 $m^2$ . How many bricks of dimensions $22.5cm\times10cm\times7.5cm$ can be painted out of this container?
Question 31 :
The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.
Question 32 :
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 33 :
State true or false: Cylinder whose radius = r, height = h, it's total surface area should be $2\pi rh$.
Question 34 :
State true or false: Curved surface area of hemisphere is $2\pi r^{2}$.
Question 35 :
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 36 :
The radius of a sphere is 2r, then its volume will be
Question 37 :
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 38 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23af59b460d7261f56d.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 outer curved surface area.Assume $\pi$ =$\frac{22}{7}$.
Question 39 :
Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25cm\times20cm\times5cm$ and the smaller of dimensions $15cm\times12cm\times5cm$. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs. 4 for 1000 $cm^2$ , find the cost of cardboard required for supplying 250 boxes of each kind.
Question 40 :
Find the curved surface area of a hemisphere of radius 21 cm.
Question 41 :
A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m × 25 m × 15 m. For how many days will the water of this tank last?
Question 42 :
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 43 :
Find the volume of a sphere whose radius is 7 cm.
Question 44 :
How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
Question 45 :
State true or false: In a right circular cone, height, radius and slant height do not always be sides of a right triangle.
Question 46 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23ef59b460d7261f572.jpeg' />
In the above image, a right circular cylinder just encloses a sphere of radius r. Find the ratio of the surface area of the sphere to the curved surface area of the cylinder.
Question 47 :
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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 48 :
Find the length of the longest pole that can be put in a room of dimensions(10 m × 10 m × 5m).
Question 49 :
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?
Question 50 :
Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.