Question 1 :
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 2 :
<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 3 :
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 4 :
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 5 :
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 6 :
A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 $cm^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?

Question 7 :
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 8 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b93273b2305849799cf.jpg' /> The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the above figure is $\frac{1}{3}\pi r^2\left[3h-2r\right]$.

Question 9 :
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 10 :
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 11 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3a273b230584979a9a.JPG' /> In the above diagram, a gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm

Question 12 :
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 13 :
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

Question 14 :
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 15 :
A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8 cm. The height of the cone is

Question 16 :
During conversion of a solid from one shape to another, the volume of the new shape will

Question 17 :
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

Question 18 :
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is

Question 19 :
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 20 :
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 21 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2e273b230584979a8c.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. The base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m. Further, suppose the machinery in the shed occupies a total space of 300 $m^3$, and there are 20 workers , each of whom occupy about 0.08 $m^3$ space on an average. Then, how much air is in the shed? (Take $\pi$ = $\frac{22}{7}$ )

Question 22 :
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. (Use $\pi$ = 3.14)

Question 23 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c31273b230584979a8f.jpg' /> In the above image, a solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. (Take $\pi$ = 3.14)

Question 24 :
A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is $4\pi rh+4\pi r^2$.

Question 25 :
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $cm^2$ .

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 :
What is the formulae for curved surface area of the frustum of the cone? (where l=slant height of frustum, $r_1$ and $r_2$ are radii of the two bases (ends) of the frustum)

Question 28 :
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 29 :
A cylindrical bucket of height 32 cm and base radius 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 and slant height of the heap.

Question 30 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b32273b230584979950.jpeg' /> 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, then find the area of material used for making it.