Sample QuestionsSimilarity (As a Size Transformation) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two similar cylindrical tins have base radii of 6 cm and 8 cm respectively. Find the capacity of the smaller tin, if the capacity of the larger tin is $256 \mathrm{~cm}^3$.
View full solution →Two similar jugs have heights of 4 cm and 6 cm respectively. If the capacity of the smaller jug is $48 \mathrm{~cm}^3$, find the capacity of the larger jug.
View full solution →The model of a building is constructed with scale factor $1: 30$.
(i) If the height of the model is 80 cm , find the actual height of the building in metre.
(ii) If the actual volume of the tank on the top of the building is $27 \mathrm{~m}^3$, find the volume of the tank on the top of the model.
View full solution →Two bottles of sauce of circular cross-section are completely similar in every respect. One is 24 cm high and the other is 32 cm high.
(i) Calculate the external diameter of the smaller bottle, given that the corresponding diameter for the other bottle is 8 cm .
(ii) The smaller bottle can hold $270 \mathrm{~cm}^3$ of sauce. How much sauce can the bigger bottle hold?
View full solution →The surface area of a solid is $5 \mathrm{~m}^2$, while the surface area of its model is $20 \mathrm{~cm}^2$. Find.
(i) the scale factor
(ii) the volume of the solid if the volume of the model is $100 \mathrm{~cm}^3$.
View full solution →The dimensions of the model of a multistoreyed building are $1 \ m \times 60 \ cm \times 1.25 \ m.$ If the model is drawn to a scale
$1 : 60,$ find the actual dimensions of the model in metres. Also find
$(i)$ the floor area of a room of the building, whose area in the model is $250 \ cm^2.$
$(ii)$ the volume of the room in the model whose actual volume is $648 \ m^3.$
View full solution →The scale of a model ship is $1 : 300.$
$(i)$ If the length of the model is $250 \ cm,$ find the actual length in $m.$
$(ii)$ If the deck area of the model is $1 m^2,$ find the deck area of the ship and the cost of painting it at $₹10$ per $m^2.$
$(iii)$ If the volume of the ship is $10,80,00,000 m^3,$ find the volume of the model.
View full solution →On a map drawn to a scale of $1 : 25,000,$ a rectangular plot of land $ABCD$ has the following measurements.
$AB = 12 \ cm, BC = 16 \ cm.$
$(i)$ The diagonal distance of the plot in $\ km.$
$(ii)$ The area of the plot in $\ km^2.$
View full solution →On a map drawn to a scale of $1: 2,50,000$ a triangular plot of land has the following measurements:
$\mathrm{AB}=3 \mathrm{~cm}, \mathrm{BC}=4 \mathrm{~cm}, \angle \mathrm{ABC}=90^{\circ}$
Calculate : (i) the actual length of AB in km (ii) the area of the plot in $\mathrm{km}^2$.
View full solution →The model of a ship is made to a scale $1: 200$
(i) The length of the model is 4 m . Calculate the length of the ship.
(ii) The area of the deck of the ship is $1,60,000 \mathrm{~m}^2$. Find the area of the deck of the model.
(iii) The volume of the model is 200 litres. Calculate the volume of the ship in $\mathrm{m}^3$.
View full solution →Let the map of a plane figure be drawn to the scale $1: p$. Then scale factor $k=$ ___________ , length in the map $=k \times$ (Actual length).
- A
$\frac{p}{1}$
- B
$\frac{1}{p}$
- C
$\frac{1}{k}$
- D
$k$
View full solution →If scale factor, $k=\frac{1}{p}$, then area of the model $=$ ___________ $\times$ (area of the actual figure).
- A
$k^2$
- B
$k$
- C
$k^2$
- D
$\frac{1}{p}$
View full solution →In case of solids, we have volume of the resulting figure $=$ ___________ $\times$ (volume of the given figure), where $k$ is the scale factor.
View full solution →The transformation is an ___________ , if $k=1$ where $k$ is the scale factor of a given size transformation.
View full solution →Each side of the resulting figure $=$ ___________ times the corresponding side of the given figure.
View full solution →Assertion (A) : If the map of a plane figure is drawn to the scale $1: p$, then, actual area of the map is given by $p^2 \times$ area in the map.
Reason (R) : In case of a map, scale factor is always greater than 1.
- A
- B
- C
Both A and R are true, and R is the correct reason for A .
- ✓
Both A and R are true, and R is incorrect reason for A .
Answer: D.
View full solution →Assertion (A) : In a size transformation, if the scale factor is $>1$, then the transformation is an enlargement.
Reason (R) : In a size transformation, a given figure is either enlarged or reduced.
- ✓
- B
- C
Both A and R are true, and R is the correct reason for A .
- D
Both A and R are true, and R is incorrect reason for A .
Answer: A.
View full solution →