Exercise 7.3 - Chapter 7 Mensuration 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $7.3$
Question $1 .$
Find the volume of a cuboid whose dimensions are
(i) length $=12 \mathrm{~cm}$, breadth $=8 \mathrm{~cm}$, height $=6 \mathrm{~cm}$
(ii) length $=60 \mathrm{~m}$, breadth $=25 \mathrm{~m}$, height $=1.5 \mathrm{~m}$
Solution:
(i) $\mathrm{l}=12 \mathrm{~cm}$
$\mathrm{b}=8 \mathrm{~cm}$
$h=6 \mathrm{~cm}$
Volume of the cuboid $=\mathrm{lbh}$
$=12 \times 8 \times 6 \mathrm{~cm}^{3}=576 \mathrm{~cm}^{3}$
(ii) $\mathrm{l}=60 \mathrm{~m}$
b $=25 \mathrm{~m}$
$\mathrm{h}=1.5 \mathrm{~m}$
Volume of the cuboid $=\mathrm{lbh}=60 \times 25 \times 1.5 \mathrm{~m}^{3}=2250 \mathrm{~m}^{3}$
 

Question $2 .$
The dimensions of a match box are $6 \mathrm{~cm} \times 3.5 \mathrm{~cm} \times 2.5 \mathrm{~cm}$. Find the volume of a packet containing 12 such match boxes.
Solution:
Dimensions of a match box $=6 \mathrm{~cm} \times 3.5 \mathrm{~cm} \times 2.5 \mathrm{~cm}$
$\mathrm{V}=(6 \times 3.5 \times 2.5) \mathrm{cm}^{3}=52.5 \mathrm{~cm}^{3}$
Volume of 12 such boxes $=12 \times 52.5 \mathrm{~cm}^{3}=630 \mathrm{~cm}^{3}$

Question $3 .$
The length, breadth and height of a chocolate box are in the ratio $5: 4: 3$. If its volume is $7500 \mathrm{~cm}^{3}$, then find its dimensions.
Solution:
Let 1 ratio $=\mathrm{x}$ then $5: 4: 3$

$\begin{aligned}
\Rightarrow 5 x: 4 x: 3 x & \\
5 x \times 4 x \times 3 x=& 60 x^{3}=7500 \mathrm{~cm}^{3} \\
& \frac{125}{375} \\
x^{3}=& \frac{7500}{60}=125 \mathrm{~cm}^{3}
\end{aligned}$
$\mathrm{x}=5 \mathrm{~cm}$ $\therefore 5 \mathrm{x}=5 \times 5=25 \mathrm{~cm}$ $4 \mathrm{x}=4 \times 5=20 \mathrm{~cm}$ $3 \mathrm{x}=3 \times 5=15 \mathrm{~cm}$ $\therefore$ Dimensions of a chocolate box are $25 \mathrm{~cm} \times 20 \mathrm{~cm} \times 15 \mathrm{~cm}$

Question $4 .$
The length, breadth and depth of a pond are $20.5 \mathrm{~m}, 16 \mathrm{~m}$ and $8 \mathrm{~m}$ respectively. Find the capacity of the pond in litres.
Solution:
$\mathrm{l}=20.5 \mathrm{~m}$
$\mathrm{b}=16 \mathrm{~m}$
$\mathrm{h}=8 \mathrm{~m}$
$\therefore$ Capacity $=$ Volume $=\mathrm{lb} \mathrm{h}=(20.5 \times 16 \times 8) \mathrm{m}^{3}=2624 \mathrm{~m}^{3}$
$1 \mathrm{~m}^{3}=1000$ litres
$\therefore 2624 \mathrm{~m}^{3}=2624000$ litres

Question $5 .$
The dimensions of a brick are $24 \mathrm{~cm} \times 12 \mathrm{~cm} \times 8 \mathrm{~cm}$. How many such bricks will be required to build a wall of $20 \mathrm{~m}$ length, $48 \mathrm{~cm}$ breadth and $6 \mathrm{~m}$ height?
Solution:
$\mathrm{l}=24 \mathrm{~cm}$
$\mathrm{b}=12 \mathrm{~cm}$
$\mathrm{h}=8 \mathrm{~cm}$
Volume of the brick $=\mathrm{lbh}=(24 \times 12 \times 8) \mathrm{cm}^{3}=2304 \mathrm{~cm}^{3}$
Wall dimensions are :
$\mathrm{L}=20 \mathrm{~m}=2000 \mathrm{~cm}$
$\mathrm{B}=48 \mathrm{~cm}$
$\mathrm{H}=6 \mathrm{~m}=600 \mathrm{~cm}$

No. of bricks required to build the wall $=\frac{\text { Volume of the wall }}{\text { Volume of a bricks, }}$

No. of bricks required $=25000$

Question $6 .$
The volume of container is $1440 \mathrm{~m}^{3}$. The length and breadth of the container are $15 \mathrm{~m}$ and $8 \mathrm{~m}$ respectively. Find its height.
Solution:
$\begin{aligned}
&V=1 \times b \times h=1440 \mathrm{~m}^{3} \\
&15 \times 8 \times h=1440
\end{aligned}$

Question $7 .$
Find the volume of a cube each of whose side is
(i) $5 \mathrm{~cm}$
(ii) $3.5 \mathrm{~m}$
(iii) $21 \mathrm{~cm}$
Solution:
(i) side of a cube (a) $=5 \mathrm{~cm}$
Volume of a cube $\mathrm{V}=\mathrm{a}^{3}=5 \times 5 \times 5=125 \mathrm{~cm}^{3}$
(ii) $\mathrm{a}=3.5 \mathrm{~m}$
$V=\mathrm{a}^{3}=3.5 \times 3.5 \times 3.5 \mathrm{~m}^{3}=42.875 \mathrm{~m}^{3}$
(iii) $\mathrm{a}=21 \mathrm{~cm} 23=21 \times 21 \times 21 \mathrm{~cm}^{3}=9261 \mathrm{~cm}^{3}$
 

Question $8 .$
A cubical milk tank holds 125000 litres of milk. Find the length of its side in metres.
Solution:
$\begin{aligned}
&\mathrm{V}=\mathrm{a}^{3}=125000 \text { litres }=125 \mathrm{~m}^{3} \\
&a=\sqrt[3]{125 \mathrm{~m}^{3}}=\sqrt[3]{5 \times 5 \times 5}
\end{aligned}$
$\therefore$ length of its side $=5 \mathrm{~m}$.

Question $9 .$
A metallic cube with side $15 \mathrm{~cm}$ is melted and formed into a cuboid. If the length and height of the cuboid is $25 \mathrm{~cm}$ and $9 \mathrm{~cm}$ respectively then find the breadth of the cuboid.
Solution:
The volume of the cuboid formed = The volume of the cube melted.
$l b h=a^{3}$