Question 1 :
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 2 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2f273b230584979a8d.JPG' /> In the above image, a juice seller was serving his customers using glasses as shown. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass . (Use $\pi$ = 3.14.)

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

Question 4 :
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 5 :
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Question 6 :
<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 7 :
A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Question 8 :
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 9 :
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 10 :
What is the formulae for curved surface area of solid hemisphere?

Question 11 :
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 12 :
<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 13 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c31273b230584979a90.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. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take $\pi$ = 3.14)

Question 14 :
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 15 :
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 16 :
<img style='object-fit:contain' src='61b19b28273b23058497994c' /> As shown in the above figure, a medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and its diameter is 5 mm. Find its surface area.

Question 17 :
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.

Question 18 :
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 19 :
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 $cm^3$ . Check whether she is correct, taking the above as the inside measurements, and $\pi$ = 3.14.

Question 20 :
A cylindrical pencil sharpened at one edge is the combination of

Question 21 :
<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 22 :
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 23 :
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 24 :
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 25 :
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.