Question 1 :
If two solid hemispheres of same radius r are joined together along their bases, then curved surface area of this new solid is

Question 2 :
Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is $12a^2$.

Question 3 :
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

Question 4 :
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is $\frac{4}{3}\pi a^3$.

Question 5 :
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. (Note that the base of the tent will not be covered with canvas.)

Question 6 :
If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is $\pi r\sqrt{h^2+r^2}+2\pi rh$ .

Question 7 :
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Question 8 :
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Question 9 :
Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Question 10 :
A cylindrical pencil sharpened at one edge is the combination of

Question 11 :
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km /h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Question 12 :
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km /h, in how much time will the tank be filled?

Question 13 :
A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.

Question 14 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Question 15 :
Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is $12\sqrt{3}$ cm. Find the edges of the three cubes.

Question 16 :
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Question 17 :
A cubical ice cream brick of edge 22 cm is to be distributed among some children by filling ice cream cones of radius 2 cm and height 7 cm upto its brim. How many children will get the ice cream cones?

Question 19 :
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Question 20 :
What is the formulae for curved surface area of solid hemisphere?

Question 21 :
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

Question 22 :
A toy is in the form of a cone of radius 3.5 cm surmounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Question 23 :
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

Question 24 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b31273b23058497994e.jpeg' /> As shown in the above figure, a gulabjamun contains sugar syrup upto about 30% of its volume. Find approximately how much syrup would be found in 45 gulabjamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

Question 25 :
A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per $dm^2$.