Question 1 :
A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume of the double cone so formed.

Question 2 :
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Question 3 :
A well of diameter 3 m is dug 14 m deep. The Earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Question 4 :
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 5 :
The curved surface area of a frustum of a cone is $\pi l\left(r_1+r_2\right)$, where l=$\sqrt{h^2+r_1^2+r_2^2}$ , $r_1$ and $r_2$ are the radii of the two ends of the frustum and h is the vertical height.

Question 6 :
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is $\pi r\left[\sqrt{r^2+h^2}+3r+2h\right]$

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b94273b2305849799d1.jpg' /> Two solid cones A and B are placed in a cylinderical tube as shown in the above figure.The ratio of their capacities are 2:1 and 6 cm is the daimeter of cone. Find the capacities of cones.

Question 8 :
2 cubes each of volume 64 $cm^3$ are joined end-to-end. Find the surface area of the resulting cuboid.

Question 9 :
A hemispherical tank full of water is emptied by a pipe at the rate of $3\frac{4}{7}$ litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take $\pi$ = $\frac{22}{7}$ )

Question 10 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c33273b230584979a92.JPG' /> The radii of the ends of a frustum of a cone 45 cm high are 28 cm and 7 cm (see the above image). Find its volume(Take $\pi$ = $\frac{22}{7}$ ).

Question 12 :
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 13 :
A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?

Question 14 :
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 15 :
Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

Question 16 :
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice.

Question 17 :
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

Question 18 :
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8}$ space of the cube remains unfilled. Then the number of marbles that the cube can accomodate is

Question 19 :
A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 20 per litre.

Question 20 :
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Question 21 :
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

Question 22 :
In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 $km^2$, check whether the total rainfall is approximately equivalent to the addition to the the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep .

Question 23 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b33273b230584979951.jpeg' /> In the above image, an oil funnel made of tin sheet consists of 10 cm long cylindrical portion attached to frustum of a cone. If the total height is 22 cm and the diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, then find the area of the tin sheet required to make the funnel.

Question 24 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b96273b2305849799d3.jpg' /> An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in the above figure. Calculate the volume of ice cream, provided that its $\frac{1}{6}$ part is left unfilled with ice cream.

Question 25 :
If two solid hemispheres of same radius r are joined together along their bases, then curved surface area of this new solid is

Question 26 :
Two identical cubes each of volume 64 $cm^3$ are joined together end to end. What is the surface area of the resulting cuboid?

Question 27 :
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 28 :
The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.

Question 29 :
What is the formulae for total surface area of solid hemisphere?

Question 30 :
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius of the heap.