Question 1 :
The diameter of a sphere is decreased by $25\%$. By what per cent does its curved surface area decrease?
Question 2 :
30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find volume of the cylinder so formed.
Question 3 :
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. Find the ratios of the surface areas of the balloon in the two cases.
Question 4 : <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 5 :
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 6 :
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 7 :
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 8 :
Find the volume of a sphere whose surface area is 154 $cm^2$ .
Question 9 : <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 10 :
The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.
Question 11 :
The radius of a sphere is 2r, then its volume will be
Question 12 :
How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?
Question 13 :
State true or false: Cone having height = h, radius = r and slant height = l, should have the curved surface area of $\pi rl$.
Question 14 :
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per $m^3$.
Question 15 :
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is first revolved about the side 12 cm and then about the side 5 cm. Find the ratio of the volumes of the two solids obtained.
Question 16 :
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 17 :
State true or false: Cylinder whose radius = r, height = h, it's total surface area should be $2\pi rh$.
Question 18 :
Curved surface area of a cone is 308 $cm^2$ and its slant height is 14 cm. Find radius of the base.
Question 19 :
Find the volume of the right circular cone with radius 6 cm, height 7 cm.
Question 20 :
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?Assume $\pi$ =$\frac{22}{7}$.
Question 21 :
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 22 :
A shopkeeper has one spherical laddoo of radius 5cm. With the same amount of material, how many laddoos of radius 2.5 cm can be made?
Question 23 :
State true or false: If the edge of the cube is a, then Diagonal of cube = $a\sqrt3$
Question 24 :
Find the volume of a sphere whose radius is 0.63 m.
Question 25 :
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 volume of the air inside the dome.
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 :
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 28 :
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 29 :
A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent.
Question 30 :
State true or false: If the radius of a cylinder is doubled and its curved surface area is not changed, then height must be halved.
Question 31 :
Find the surface area of a sphere of radius 5.6 cm.
Question 32 :
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 33 :
A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume of the solid so formed.
Question 34 :
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 35 :
The height of a cone is 15 cm. If its volume is 1570 $cm^3$ , find the radius of the base. (Use $\pi$ = 3.14)
Question 36 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Lateral surface area of cuboid = 2 h (l + b)
Question 37 :
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 38 :
If we cut out many of the plane figures and stack them up in a vertical pile is called ______
Question 39 :
A cloth having an area of 165 $m^2$ is shaped into the form of a conical tent of radius 5 m. How many students can sit in the tent if a student, on an average, occupies $\frac{5}{7} m^2$ on the ground?
Question 40 :
Find the total surface area of a hemisphere of radius 21 cm.
Question 41 :
State true or false: If the edge of the cube is a, then Total surface area of cube = $6a^{2}$
Question 42 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d235f59b460d7261f565.jpeg' />
In the above image, Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is Rs 360 per dozen.
Question 43 :
Find the surface area of a sphere of diameter 21 cm.
Question 44 :
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 45 :
Find the surface area of a sphere of radius 7 cm.
Question 46 :
Find how much steel was actually used, if $\frac{1}{12}$ of the steel actually used was wasted in making the tank that is 4.2 m in diameter and 4.5 m high.Assume $\pi$ =$\frac{22}{7}$.
Question 47 :
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 48 :
Find the surface area of a sphere of diameter 3.5 m.
Question 49 :
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find its inner curved surface area.Assume $\pi$ =$\frac{22}{7}$.
Question 50 :
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.
