Question 1 :
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 2 :
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 3 :
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Question 4 :
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Question 5 :
A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is

Question 6 :
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 7 :
Water in a canal, 6 m wide and 1.5 m deep is flowing at a speed of 10 km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Question 8 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$ is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, find the length of the wire.

Question 9 :
A cone of radius 4 cm is divided into two parts by drawing a plane through the mid point of its axis and parallel to its base. Compare the volumes of the two parts.

Question 10 :
<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 11 :
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 12 :
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 13 :
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 14 :
<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 15 :
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 16 :
What is the formulae for curved surface area of solid hemisphere?

Question 17 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b94273b2305849799d0.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 cylinder. Find the heights cones.

Question 18 :
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 19 :
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 20 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b30273b23058497994d.jpeg' /> As shown in the above figure, a wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, then find the total surface area of the article.

Question 21 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b92273b2305849799ce.jpg' /> Actual capacity of a vessel as shown in the above figure is equal to the difference of volume of the cylinder and volume of the hemisphere.

Question 22 :
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 23 :
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 24 :
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 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.

Question 26 :
A metallic right circular cone 20 cm high and whose vertical angle is $60^{\circ}$, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $\frac{1}{16}$ cm, then find the length of the wire.

Question 27 :
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

Question 28 :
A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is

Question 29 :
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 30 :
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.