Question 1 : <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 2 :
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 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c37273b230584979a97.JPG' />
In the above image, 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 the diameter of the capsule is 5 mm. Find its surface area.
Question 4 :
A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.
Question 5 :
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled?
Question 6 :
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 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c35273b230584979a94.JPG' />
In the above image, hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see the above image). If each cubic cm of molasses has mass about 1.2 g, find the mass of the molasses that can be poured into each mould. (Take $\pi$ =$\frac{22}{7}$)
Question 8 :
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 9 :
What is the formulae for volume of the frustum of the cone? (where h = vertical height of the frustum, $r_1$ and $r_2$ are radii of the two bases (ends) of the frustum)
Question 10 :
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 11 :
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 12 :
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 13 : <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 14 :
2 cubes each of volume 64 $cm^3$ are joined end to end. Find the surface area of the resulting cuboid.
Question 15 :
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have?
Question 16 :
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 metal sheet used to make the container, if it costs Rs 8 per 100 $cm^2$ .
Question 17 :
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length of the wire, assuming the density of copper to be 8.88 g per $cm^3$ .
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c36273b230584979a95.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 total surface area(Take $\pi$ = $\frac{22}{7}$ ).
Question 19 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b8f273b2305849799ca.jpg' />
In the above figure, the shape of a gilli, in the gilli-danda game, is a combination of
Question 20 :
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 21 :
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 22 :
Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
Question 23 : <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 25 :
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water.The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket
Question 26 :
A toy is in the form of a cone of radius 3.5 cm mounted 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 27 :
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 28 :
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
Question 29 :
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 30 :
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 31 :
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 32 :
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 33 :
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 34 : <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 35 :
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 36 :
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 cost of the canvas of the tent at the rate of Rs 500 per $m^2$ . (Note that the base of the tent will not be covered with canvas.)
Question 37 :
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
Question 38 :
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
Question 39 : <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 40 :
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 41 :
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 42 :
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.
Question 43 :
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 44 :
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 45 :
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions $5.5 cm\times 10 cm\times 3.5 cm$?
Question 46 : <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 47 : <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 48 :
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 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c2b273b230584979a89.JPG' />
In the above image, the decorative block shown is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $\pi$ = $\frac{22}{ 7}$ )
Question 50 :
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.
