A cube of side 5 cm is palnted on all its faces. If it is sliced into cubes of side 1 cm, then how many cubes of side 1 cm will have exactly one of their faces painted?
- A27
- B42
- ✓54
- D142
Answer: C.
View full solution →Question types
Mensuration question types
108 questions across 10 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
108
Questions
10
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
14 Q→02TRUE-FLASE [1 Marks Each]
5 Q→03Assertion (A) & Reason (B) MCQ
3 Q→042 Marks Questions
35 Q→053 Marks Question
30 Q→065 Marks Questions
9 Q→07MATCH THE FOLLOWING.
1 Q→08BLANKS [1 Marks Each]
5 Q→094 Mark Question
5 Q→10case /data -based (4 Marks)
1 Q→Sample Questions
Mensuration questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The heights of two right circular cylinders are the same. Their volumes are $16 \pi m^3$ and $81 \pi m^3$. The ratio of their base radii is
- A$16: 81$
- ✓$4: 9$
- C$2: 3$
- D$9: 4$
Answer: B.
View full solution →The surface area of the six faces of a rectangular solid are $16,16,32,32,72$ and $72 cm^2$. The volume of the solid (in $cm ^3$ ) is
- ✓192
- B480
- C384
- D2592
Answer: A.
View full solution →The dimensions of a godown are 40 m, 25 m and 10 m . If it is filled with cuboidal boxes each of dimensions 2 m × 1.25 m × 1 m, then the number of boxes will be
- A1800
- B2000
- ✓4000
- D8000
Answer: C.
View full solution →If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true?
- AVolume of the cylinder will be doubled
- ✓Volume of the cylinder will remain unchanged
- CVolume of the cylinder will be halved
- DVolume of the cylinder will be $\frac{1}{4}$ of the original volume
Answer: B.
View full solution →The area of trapezium becomes 4 times, if its height gets doubled.
The areas of any two faces of a cuboid are equal.
The areas of any two faces of a cube are equal.
A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cm cubes, then number of such cubes that will have exactly two of their faces painted is 24 .
The lateral surface area of a cuboid whose length is 5 m , breadth is 4 m and height is 2 m , is $36 m^2$.
View full solution →Assertion (A) 8 persons can stay in a cubical room. Each person required $64 m^3$ of air. The side of cube is 8 m .
Reason (R) The surface area of cube can be represented as $6 s^2$, since a cube has six side and surface area of each side is represented by its length.
Reason (R) The surface area of cube can be represented as $6 s^2$, since a cube has six side and surface area of each side is represented by its length.
- ABoth A and R are true and R is correct explanation of A.
- ✓Both A and R are true but R is not correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: B.
View full solution →Assertion (A) The total surface area of a cylinder of base radius $r$ and height $h$ is $2 \pi r(r+h)$.
Reason (R) The surface area formula is a mathematical solution to find the total area of any three dimensional object occupied by all of its surface.
Reason (R) The surface area formula is a mathematical solution to find the total area of any three dimensional object occupied by all of its surface.
- ✓Both A and R are true and R is correct explanation of A.
- BBoth A and R are true but R is not correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion (A) Area of rhombus whose side is 5 cm and altitude is 3 cm is $15 cm^2$.
Reason (R) Area of thombus is sometimes equal to the area of parallelogram as every parailelogram is rhombus.
Reason (R) Area of thombus is sometimes equal to the area of parallelogram as every parailelogram is rhombus.
- ABoth A and R are true and R is correct explanation of A.
- BBoth A and R are true but R is not correct explanation of A.
- ✓A is true but R is false.
- DA is false but R is true.
Answer: C.
View full solution →Find the volume of the following cylinders.
Find the surface area of cube (i) and lateral surface area of cube (ii).
Find the total surface area of the following cuboids.
Find the area of polygon $M N O P Q R$, If $M P=9 cm$, $M D=7 cm, M C=6 cm$, $M B=4 cm, M A=2 cm . N A O C$, $Q D$ and $R B$ are perpendiculars to diagonal MP.
View full solution →After the surface area of a cube is painted, the cube is cut into 64 smaller cubes of same dimensions (see the figure). How many have
(i) no face painted? $\qquad$ (ii) 1 face painted? $\qquad$
(iii) 2 faces painted? $\qquad$ (iv) 3 faces painted?
View full solution →(i) no face painted? $\qquad$ (ii) 1 face painted? $\qquad$
(iii) 2 faces painted? $\qquad$ (iv) 3 faces painted?
Find the volume of the following cubes
(I) with a side of 4 cm .
(ii) with a side of 1.5 m .
(I) with a side of 4 cm .
(ii) with a side of 1.5 m .
Find the volume of the following cuboids.
Take 36 cubes of equal size (i.e. length of each cube is same). Arrange them to form a cuboid. You can arrange them In many ways.
Observe the following table and fill in the blanks.
Observe the following table and fill in the blanks.
Find the total surface area of the following cylinders.
Note that lateral surface area of a cylinder is the circumference of base $\times$ height of cylinder. Can we write lateral surface area of a cuboid as Perimeter of base $\times$ Height of cuboid?
View full solution →Polygon ABCDE is divided into parts as shown.
Find its area, if $A D=8 cm, A H=6 cm, A G=4 cm$, $A F=3 cm$ and perpendiculars $B F=2 cm$, $C H=3 cm, E G=2.5 cm$.
Area of polygon $A B C D E=$ Area of $\triangle A F B+$
Area of $\triangle A F B=\frac{1}{2}, A F, B F=\frac{1}{2}, 3 \times 2=$
Area of trapezium
$\begin{aligned} F B C H & =F H \times \frac{(B F+C H)}{2} \\ & =3 \times \frac{(2+3)}{2}+\ldots\end{aligned}$
$\ [F H=A H-A F]$
Area of $\triangle C H D=\frac{1}{2} \times H D \times C H=\ldots$;
Area of $\triangle A D E=\frac{1}{2} \times A D \times G E=\ldots$
So, the area of polygon $A B C D E=\ldots$
View full solution →Find its area, if $A D=8 cm, A H=6 cm, A G=4 cm$, $A F=3 cm$ and perpendiculars $B F=2 cm$, $C H=3 cm, E G=2.5 cm$.
Area of polygon $A B C D E=$ Area of $\triangle A F B+$
Area of $\triangle A F B=\frac{1}{2}, A F, B F=\frac{1}{2}, 3 \times 2=$
Area of trapezium
$\begin{aligned} F B C H & =F H \times \frac{(B F+C H)}{2} \\ & =3 \times \frac{(2+3)}{2}+\ldots\end{aligned}$
$\ [F H=A H-A F]$
Area of $\triangle C H D=\frac{1}{2} \times H D \times C H=\ldots$;
Area of $\triangle A D E=\frac{1}{2} \times A D \times G E=\ldots$
So, the area of polygon $A B C D E=\ldots$
Divide the following polygons into parts (triangles and trapezium) to find out its area.
A company sells biscuits. For packing purpose they are using cuboidal boxes : Box $A \rightarrow 3 cm \times 8 cm \times 20 cm$ and Box $B \rightarrow 4 cm \times 12 cm \times 10 cm$. What size of the box will be economical for the company? Why? Can you suggest any other size (dimensions) which has the same volume but is more economical than these?
View full solution →How will you arrange 12 cubes of equal length to form a cuboid of smallest surface area?
| Column A | Column B | ||
| (a) | Area of a parallelogram is | (i) | $\pi r^2$, where $r$ is the radius |
| (b) | Area of trapezium is | (ii) | Base $\times$ Corresponding height |
| (c) | Area of rhombus is | (iii) | $\frac{1}{2} \times$ Sum of parallel sides $\times$ height |
| (d) | Area of a circle is | (iv) | $\frac{1}{2} \times$ Product of diagonals |
A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of cube is __________
All six faces of a cuboid are __________ in shape and of __________ area.
Opposite faces of a cuboid are __________ in area.
Volume of a cylinder with radius $r$ and height $h$ is __________
View full solution →Area of rhombus $=\frac{1}{2} \times$ Product of __________ .
View full solution →A suitcase with measures $80 cm \times 48 cm \times 24 cm$ is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?
TIPS Firstly, find the total surface area of 1 suitcase. Here, the area of cloth used to cover 1 suitcase will be equal to surface area of 1 suitcase. Use this result to find the length of cloth required for 1 suitcase and then multiply it by 100 to get required length of cloth to cover 100 suitcases.
View full solution →TIPS Firstly, find the total surface area of 1 suitcase. Here, the area of cloth used to cover 1 suitcase will be equal to surface area of 1 suitcase. Use this result to find the length of cloth required for 1 suitcase and then multiply it by 100 to get required length of cloth to cover 100 suitcases.
Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area of each sail of the sailboats to the nearest tenth.
Word Maze
Find the names of the solids from the given word mare whose areas or volumes are given below by colouring the boxes using the given colour code
View full solution →Find the names of the solids from the given word mare whose areas or volumes are given below by colouring the boxes using the given colour code
| S.No | Area/Volume | Colour Code |
| 1 | $\frac{1}{2} d_1 \times d_2$ | red |
| 2 | $l b h$ | blue |
| 3 | $\pi r^2 h$ | yelloe |
| 4 | $\pi r^2$ | green |
| 5 | $\frac{1}{2} b h$ | orange |
| 6 | $\frac{1}{2}(a+b) \times h$ | pink |
Find the area of the shaded portion in the following figure.
A rectangular sheet of a paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case, if the sheet measures $44 cm \times 33 cm$.
View full solution →The figure below shows a blueprint of a shower room of a club.
The walls of the shower room (inner boundary) is 0.1 m thick. The wall of outer boundary is 0.2 m thick.
On the basis of above given information, answer the following questions.
Q.1. The inside wall and the floor of the shower room are covered with tiles. What area of the shower room is covered with tiles?
(a) $20.54 m^2$ $\qquad$ (c) $57.5 m^2$
(b) $37.52 m^2$ $\qquad$ (d) $65.20 m^2$
Q.2. Which of the following calculations shows the inside volume (in $m ^3$ ) of the shower room?
(a) $79 \times 2.6 \times 1.76$ $\qquad$ (b) $7.9 \times 31 \times 1.76$
(c) $8.2 \times 3.1 \times 1.76$ $\qquad$ (d) $8.5 \times 4.2 \times 1.76$
Q.3. An area is marked for cupboards.
How many cupboards with dimensions $1.5 \times 0.6 \times 1.76$ (length $\times$ breadth $\times$ height) can be built in the area?
Q.4. One litre of paint is required to paint 12 sq m . Approximately, how many litres of paint are required to paint the outer boundary of the shower room?
(a) 3 $\qquad$ (b) 5 $\qquad$
(c) 60 $\qquad$ (d) 89
View full solution →The walls of the shower room (inner boundary) is 0.1 m thick. The wall of outer boundary is 0.2 m thick.
On the basis of above given information, answer the following questions.
Q.1. The inside wall and the floor of the shower room are covered with tiles. What area of the shower room is covered with tiles?
(a) $20.54 m^2$ $\qquad$ (c) $57.5 m^2$
(b) $37.52 m^2$ $\qquad$ (d) $65.20 m^2$
Q.2. Which of the following calculations shows the inside volume (in $m ^3$ ) of the shower room?
(a) $79 \times 2.6 \times 1.76$ $\qquad$ (b) $7.9 \times 31 \times 1.76$
(c) $8.2 \times 3.1 \times 1.76$ $\qquad$ (d) $8.5 \times 4.2 \times 1.76$
Q.3. An area is marked for cupboards.
How many cupboards with dimensions $1.5 \times 0.6 \times 1.76$ (length $\times$ breadth $\times$ height) can be built in the area?
Q.4. One litre of paint is required to paint 12 sq m . Approximately, how many litres of paint are required to paint the outer boundary of the shower room?
(a) 3 $\qquad$ (b) 5 $\qquad$
(c) 60 $\qquad$ (d) 89
Generate a Mensuration paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.