Question 1 :
State true or false: The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.
Question 2 :
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 3 :
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 4 :
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 5 :
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
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 :
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.
Question 8 :
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 9 :
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 10 :
State true or false: The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
Question 11 :
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 12 :
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 greater lateral surface area and by how much?
Question 13 :
Rain water which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if the rain fall is 1 cm. Give your answer to the nearest integer.($\pi=3.14$)
Question 14 :
State true or false: If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
Question 15 :
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 16 :
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 17 :
Find the volume of a sphere whose radius is 0.63 m.
Question 18 :
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 19 :
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 20 :
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 21 :
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 22 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Volume of cuboid = lbh
Question 23 :
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 24 :
Find the amount of water displaced by a solid spherical ball of diameter 0.21 m.
Question 25 :
Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the ratio of S and S′.
