Find the length of the longest rod that can be placed in a room measuring 12 m 9 m 8 m.
Question types
Volume and Surface Area of Solids question types
104 questions across 5 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
104
Questions
5
Question groups
5
Question types
01
[2 Mark Question Answer]
12 Q→02[3 marks sum]
20 Q→03[4 marks sum]
21 Q→04[5 marks sum]
12 Q→05MCQ
39 Q→Sample Questions
Volume and Surface Area of Solids questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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The square on the diagonal of a cube has an area of $1875 cm^2$.
Calculate :
(i) the side of the cube,
(ii) the total surface area of the cube.
View full solution →Calculate :
(i) the side of the cube,
(ii) the total surface area of the cube.
The dimensions of a metallic cuboid are 100 cm. 80 cm 64 cm. It is melted and recast into a cube. Find
(i) the edge of the cube,
(ii) the surface area of the cube.
(i) the edge of the cube,
(ii) the surface area of the cube.
A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of third smaller cube.
Three cubes, each of side 6 cm, are joined end to end. Find the surface area of the resulting cuboid.
The dimensions of a field are 15 m 12 m. A pit 7.5 m 6 m 1.5 m is dug in one corner of the field and the earth removed from it, is evenly spread over the remaining area of the field. Calculate, by how much the level of the field is raised.
A class room is 12.5 m long, 6.4 m broad and 5 m high. How many students can it accommodate, if each student needs $1.6 m^2$ of floor area? How many cubic metres of air would each student get?
View full solution →The cross-section of a tunnel, perpendicular to its length is a trapezium ABCD in which AB = 8m DC 6 m and AL = BM The height of the tunnel is 2.4 m and its length is 40 m.
Find:
(i) the cost of paving the floor of the tunnel at 16 per m ^ 2
(ii) the cost of painting the internal surface of the tunnel, excluding the floor at the rate of 5 per $m ^2$
View full solution →Find:
(i) the cost of paving the floor of the tunnel at 16 per m ^ 2
(ii) the cost of painting the internal surface of the tunnel, excluding the floor at the rate of 5 per $m ^2$
The adjoining figure shows a solid of uniform cross section. Find the volume of the solid. It is being given that all the measurements are in cm and each angle in the figure is a right angle.
A square brass plate of side $x cm$ is 1 mm thick and weighs 5.44 kg . If $1 cm^3$ of brass weighs 8.5 g , find the value of $x$.
View full solution →The cost of papering the four walls of a room 12 m long at ₹ 6.50 per square metre is ₹ 1638 and the cost of matting the floor at ₹ 3.50 per square metre is ₹ 378. Find the height of the room.
The area of a path is $6500 m^2$. Find the cost of covering it with gravel 14 cm deep at the rate of ₹ 5.60 per cubic metre.
View full solution →The volume of a cuboid is $14400 cm^3$ and its height is 15 cm . The cross-section of the cuboid is a rectangle having its sides in the ratio $5: 3$. Find the perimeter of the cross-section.
View full solution →Find the number of bricks, each measuring $25 cm \quad 12.5 cm \quad 7.5 cm$, required to construct a wall 6 m long, 5 m high and 50 cm thick, while the cement and the sand mixture occupies $\frac{1}{20}$ th of the volume of the wall.
View full solution →The area of cross-section of a rectangular pipe is $5.4 cm^2$ and water is pumped out of it at the rate of 27 kmph . Find, in litres, the volume of water which flows out of the pipe in 1 minute.
View full solution →Manish is a carpenter. One day, he made an open cubical box of internal edge 18 cm. The thickness of the plywood is 1 cm. He painted the inner surface of the box black and the outer lateral surfaces as green.
Based on the above information, answer the following questions :
Q.1. Total area to be painted black is :
(a) $1600 cm^2$ (b) $1620 cm^2$ (c) $1650 cm^2$ (d) $1680 cm^2$
Q.2. Length of the outer edge of the box is :
(a) 20 cm (b) 19 cm (c) 18 cm (d) 18.5 cm
Q.3. Total outer lateral surface area to be painted green is :
(a) $1500 cm^2$ (b) $1510 cm^2$ (c) $1520 cm^2$ (d) $1600 cm^2$
Q.4. Total outer surface area of the box (excluding the top) is :
(a) $1900 cm^2$ (b) $1920 cm^2$ (c) $2000 cm^2$ (d) $2320 cm^2$
Q.5. Length of the longest rod that can fit inside the box is :
(a) 18 cm (b) 19 cm (c) 20 cm (d) 3 cm
View full solution → Based on the above information, answer the following questions :
Q.1. Total area to be painted black is :
(a) $1600 cm^2$ (b) $1620 cm^2$ (c) $1650 cm^2$ (d) $1680 cm^2$
Q.2. Length of the outer edge of the box is :
(a) 20 cm (b) 19 cm (c) 18 cm (d) 18.5 cm
Q.3. Total outer lateral surface area to be painted green is :
(a) $1500 cm^2$ (b) $1510 cm^2$ (c) $1520 cm^2$ (d) $1600 cm^2$
Q.4. Total outer surface area of the box (excluding the top) is :
(a) $1900 cm^2$ (b) $1920 cm^2$ (c) $2000 cm^2$ (d) $2320 cm^2$
Q.5. Length of the longest rod that can fit inside the box is :
(a) 18 cm (b) 19 cm (c) 20 cm (d) 3 cm
The length, breadth and height of Kavita's bedroom are 6 m, 4 m and 3 m respectively. It has two equal windows, each of dimensions 1 m 0.5 m. It also has a door of dimensions 2 m 1 m.
Based on the above information, answer the following questions:
Q.1. Area occupied by the door and the two windows is:
(a) $1 m^2$ (b) $2 m^2$ (c) $2.5 m^2$ (d) $3 m^2$
Q.2. Kavita wants to whitewash the four walls of the room. Area to be whitewashed is:
(a) $60 m^2$ (b) $57 m^2$ (c) $55 m^2$ (d) $50 m^2$
Q.3. Square tiles each of side 50 cm are laid on the floor of the room. The number of such tiles laid is:
(a) 100 (b) 98 (c) 96 (d) 72
Q.4. Volume of air contained in the room is:
(a) $72 m^3$ (b) $70 m^3$ (c) $60 m^3$ (d) $52 m^3$
Q.5. The length of the longest rod (to the nearest m) that can be placed in the room is:
(a) 4 m (b) 5 m (c) 8 m (d) 7 m
View full solution → Based on the above information, answer the following questions:
Q.1. Area occupied by the door and the two windows is:
(a) $1 m^2$ (b) $2 m^2$ (c) $2.5 m^2$ (d) $3 m^2$
Q.2. Kavita wants to whitewash the four walls of the room. Area to be whitewashed is:
(a) $60 m^2$ (b) $57 m^2$ (c) $55 m^2$ (d) $50 m^2$
Q.3. Square tiles each of side 50 cm are laid on the floor of the room. The number of such tiles laid is:
(a) 100 (b) 98 (c) 96 (d) 72
Q.4. Volume of air contained in the room is:
(a) $72 m^3$ (b) $70 m^3$ (c) $60 m^3$ (d) $52 m^3$
Q.5. The length of the longest rod (to the nearest m) that can be placed in the room is:
(a) 4 m (b) 5 m (c) 8 m (d) 7 m
The adjoining figure shows a solid of uniform cross section. Find the volume of the solid. It is being given that all the measurements are in cm and each angle in the figure is a right angle.
[Hint. This consists of two cuboids of dimensions (4 $\times$ 6 $\times$ 3) $cm ^3$ and (4 $\times$ 3 $\times$ 9) $cm ^3$]
The area of cross-section of a rectangular pipe is 5.4 $cm ^2$ and water is pumped out of it at the rate of 27kmph. Find, in litres, the volume of water which flows out of the pipe in 1 minute.
View full solution →In the figure, there are fifty, 500 rupee notes in the bundle. Volume of the bundle is $98 cm^3$, length $=14 cm$ and breadth $=7 cm$. The thickness of 1 note is :
- A1 mm
- B0.1 mm
- C2 mm
- ✓0.2 mm
Answer: D.
View full solution →In the figure, four faces of the solid are shaded. The shaded area is :
- A$100 cm^2$
- B$150 cm^2$
- ✓$200 cm^2$
- D$300 cm^2$
Answer: C.
View full solution →If a cube has surface area S and volume V , then the volume of the cube of surface area 2 S is :
- A$\sqrt{2} V$
- B2 V
- ✓$2 \sqrt{2} V$
- D$\frac{ V }{\sqrt{2}}$
Answer: C.
View full solution →The volume of a cuboid of dimensions $x, y$ and $z$ is V and its surface area is S . The value of $\frac{1}{V}$ is :
- A$\frac{2}{S}\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$
- B$\frac{ S }{2}\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$
- C$\frac{3}{S}\left(\frac{1}{x}-\frac{1}{y}-\frac{1}{z}\right)$
- ✓$\frac{ S }{3}\left(\frac{a+b+c}{a b c}\right)$
Answer: D.
View full solution →The area of base of a cuboidal water tank is $6500 cm^2$ and the volume of water contained in it is $2.6 m^3$. The depth of the water is :
- A5 m
- ✓4 m
- C3.5 m
- D3 m
Answer: B.
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