Question 1 : A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the the slant height of the conical portion is 5 cm, find the volume and total surface area of the rocket.

Question 2 : 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 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b97273b2305849799d5.PNG ' /> A funnel'(see the above figure) is the combination of

Question 4 : A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by Another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 $cm^3$ of iron has approximately 8 g mass.

Question 5 : 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 upto brim. When lead shots each in the shape of a sphere with radius 0.5 cm are dropped into the vessel, the one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Question 6 : The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter.A full barrel of ink in the pen is used up on writing 3300 words on an average.How many words can be written in a bottle of ink containing one fifth of a litre?

Question 7 : A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.

Question 8 : 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, then 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 9 : <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 10 : An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.

Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b32273b23058497994f.jpeg' /> As shown in the above figure, a pen stand made of wood, is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 cm\times10 cm \times 3.5 cm$. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Question 12 : If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then how much water in $cm^3$ flows out of the cylindrical cup?

Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c32273b230584979a91.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 curved surface area(Take $\pi$ = $\frac{22}{7}$ ).

Question 14 : A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

Question 15 : How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?

Question 16 : The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

Question 17 : Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Question 18 : A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41\frac{19}{21}m^3$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?

Question 19 : 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 20 : A spherical steel ball is melted to make eight new identical balls.Then, the radius of each new ball be $\frac{1}{8}$th the radius of the original ball.

Question 21 : <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 22 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b95273b2305849799d2.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 diameter of cone.Find the volume of the remaining portion of the cylinder. (i.e. the portion excluding the cones)

Question 23 : From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Question 24 : A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.

Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3b273b230584979a9b.JPG' /> In the above image, a fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c30273b230584979a8e.JPG' /> In the above image, shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder as shown. If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, then find the volume of air that the shed can hold. (Take $\pi$ = $\frac{22}{7}$ )

Question 27 : 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 28 : A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. How much canvas cloth is required to just cover the heap?

Question 29 : <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 30 : How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.