The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5cm, then height of the cone is:
- A10cm
- ✓15cm
- C18cm
- D24cm
Answer: B.
View full solution →Question types
Surface Areas and Volumes question types
333 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
333
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
74 Q→021 Marks Question
24 Q→032 Marks Questions
18 Q→043 Marks Question
144 Q→055 Marks Questions
73 Q→Sample Questions
Surface Areas and Volumes questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If two solid-hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is:
- ✓$4\pi\text{r}^2$
- B$6\pi\text{r}^2$
- C$3\pi\text{r}^2$
- D$8\pi\text{r}^2$
Answer: A.
View full solution →The diameters of two circular ends of the bucket are 44cm and 24cm. The height of the bucket is 35cm. The capacity of the bucket is:
- ✓32.7 litres
- B33.7 litres
- C34.7 litres
- D31.7 litres
Answer: A.
View full solution →The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is:
- A$3\pi\text{r}^2$
- ✓$\frac{\pi\text{r}^3}{3}$
- C$\frac{\pi\text{r}^2}{3}$
- D$3\pi\text{r}^3$
Answer: B.
View full solution →A reservoir is in the shape of a frustum of a right circular cone. It is $8m$ across at the top and $4m$ across at the bottom. If it is $6m$ deep, then its capacity is :
- ✓$176 m^3$
- B$196 m^3$
- C$200 m^3$
- D$110 m^3$
Answer: A.
View full solution →Three solid spheres of radii 3, 4 and 5cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.
A solid piece of metal in the form of a cuboid of dimensions 11 cm x 7 cm x 7 cm is melted to form a number of a solid spheres of radii $\frac{7}{2}$ cm each. Find the value of n.
View full solution →A solid metallic sphere of radius 3 cm is melted and recast into the shape of a solid cylinder of radius 2 cm. Find the height of the cylinder.
Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes?
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
A cylindrical bucket 28cm in diameter and 72cm high is full of water. The water is emptied into a rectangular tank 66cm long and 28cm wide. Find the height of the water level in the tank.
A rectangular tank 15m long and 11m broad is required to receive entire liquid contents from a fully cylindrical tank of internal diameter 21m and length 5m. Find the least height of the tank that will serve the purpose.
A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?
$25$ circular plates, each of radius $10.5 \ cm$ and thickness $1.6 \ cm$, are placed one above the other to form a solid circular cylinder.
Find the curved surface area and the volume of the cylinder so formed.
View full solution →Find the curved surface area and the volume of the cylinder so formed.
A solid metallic sphere of radius 5.6cm is melted and solid cones each of radius 2.8cm and height 3.2cm are made. Find the number of such cones formed.
If the heights of two right circular cones are in the ratio $1 : 2$ and the perimeters of their bases are in the ratio $3 : 4$, what is the ratio of their volumes?
View full solution →A well of diameter 3m is dug $14\ m$ deep. The earth taken out of it has been spread evenly all around it to a width of $4\ m$ to form an embankment. Find the height of the embankment.
View full solution →A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3m and its height is 3.5m?
What is the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
The height of a solid cylinder is $15\ cm$ and the diameter of its base is $7\ cm$. Two equal conical holes each of radius $3\ cm$, and height $4\ cm$ are cut off. Find the volume of the remaining solid.
View full solution →The $\frac{3}{4}\text{th}$ part of a conical vessel of internal radius 5cm and height 24cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height of water in cylindrical vessel.
View full solution →An icecream cone full of icecream having radius 5cm and height 10cm as shown’in the figure. Calculate the volume of icecream, provided that its $\frac{1}{6}$ parts is left unfilled with icecream.
View full solution →The internal and external diameters of a hollow hemispherical vessel are 21cm and 25.2cm respectively. The cost of painting $1cm^2$ of the surface is 10 paise. Find the total cost to paint the vessel all over.
View full solution →In the given figure, from the top of a solid cone of height 12cm and base radius 6cm, a cone of height 4cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid.$\Big(\text{use}\ \pi=\frac{22}{7}\text{and}\sqrt{5}=2.236\Big).$
View full solution →A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is $\frac{14}{3}\text{m}$ and the diameter of hemisphere is 3.5m. Calculate the volume and the internal surface area of the solid.
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