Exercise 7.4 - Chapter 7 Mensuration 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $7.4$
Multiple Choice Questions:
Question 1.
The semi-perimeter of a triangle having sides $15 \mathrm{~cm}, 20 \mathrm{~cm}$ and $25 \mathrm{~cm}$ is
(1) $60 \mathrm{~cm}$
(2) $45 \mathrm{~cm}$
(3) $30 \mathrm{~cm}$
(4) $15 \mathrm{~cm}$
Solution:
(3) $30 \mathrm{~cm}$
Hint $: \therefore s=\frac{15+20+25}{2}=\frac{60}{2}=30$
 

Question $2 .$
If the sides of a triangle are $3 \mathrm{~cm}, 4 \mathrm{~cm}$ and $5 \mathrm{~cm}$, then the area is
(1) $3 \mathrm{~cm}^{2}$
(2) $6 \mathrm{~cm}^{2}$
(3) $9 \mathrm{~cm}^{2}$
(4) $12 \mathrm{~cm}^{2}$

Solution:
(2) $6 \mathrm{~cm}^{2}$

Question $3 .$
The perimeter of an equilateral triangle is $30 \mathrm{~cm}$. The area is
(1) $10 \sqrt{3} \mathrm{~cm}^{2}$
(2) $12 \sqrt{3} \mathrm{~cm}^{2}$
(3) $15 \sqrt{3} \mathrm{~cm}^{2}$
(4) $25 \sqrt{3} \mathrm{~cm}^{2}$
Solution:
$3 a=30$
$\mathrm{a}=10 \mathrm{~cm}$

Solution:
(4) $25 \sqrt{3} \mathrm{~cm}^{2}$
 

Question $4 .$
The lateral surface area of a cube of side $12 \mathrm{~cm}$ is
(1) $144 \mathrm{~cm}^{2}$
(2) $196 \mathrm{~cm}^{2}$
(3) $576 \mathrm{~cm}^{2}$
(4) $664 \mathrm{~cm}^{2}$
Hint: $4 \mathrm{a}^{2}=4 \times 12 \times 12=4 \times 144=576 \mathrm{~cm}^{2}$
Solution:
(3) $576 \mathrm{~cm}^{2}$
 

Question $5 .$
If the lateral surface area of a cube is $600 \mathrm{~cm}^{2}$, then the total surface area is
(1) $150 \mathrm{~cm}^{2}$
(2) $400 \mathrm{~cm}^{2}$
(3) $900 \mathrm{~cm}^{2}$
(4) $1350 \mathrm{~cm}^{2}$

Solution:
(3) $900 \mathrm{~cm}^{2}$
 

Question $6 .$
The total surface area of a cuboid with dimension $10 \mathrm{~cm} \times 6 \mathrm{~cm} \times 5 \mathrm{~cm}$ is
(1) $280 \mathrm{~cm}^{2}$
(2) $300 \mathrm{~cm}^{2}$
(3) $360 \mathrm{~cm}^{2}$
(4) $600 \mathrm{~cm}^{2}$
Hint:
$\mathrm{TSA}=2(\mathrm{lb}+\mathrm{bh}+\mathrm{hl})$
$=2(10 \times 6+6 \times 5+5 \times 10)=2(60+30+50)=2(140)=280 \mathrm{~cm}^{2}$
Solution:
(1) $280 \mathrm{~cm}^{2}$

Question $7 .$
If the ratio of the sides of two cubes are $2: 3$, then ratio of their surface areas will be
(1) $4: 6$
(2) $4: 9$
(3) $6: 9$
(4) $16: 36$
Hint:
$\begin{aligned}
&a: b=2: 3 \\
&4 a^{2}: 4 b^{2}=4 \times 2^{2}: 4: 3^{2} \\
&\Rightarrow 16: 36 \\
&\Rightarrow 4: 9
\end{aligned}$
Solution:
(2) $4: 9$

Question $8 .$
The volume of a cuboid is $660 \mathrm{~cm} 3$ and the area of the base is $33 \mathrm{~cm}^{2}$. Its height is
(1) $10 \mathrm{~cm}$
(2) $12 \mathrm{~cm}$
(3) $20 \mathrm{~cm}$
(4) $22 \mathrm{~cm}$

Solution:
(3) $20 \mathrm{~cm}$
 

Question $9 .$
The capacity of a water tank of dimensions $10 \mathrm{~m} \times 5 \mathrm{~m} \times 1.5 \mathrm{~m}$ is
(1) 75 litres
(2) 750 litres
(3) 7500 litres
(4) 75000 litres
Hint: Volume of cuboid $=1 \times b \times h$
Solution

(1) 75 litres
:
Question $10 .$
The number of bricks each measuring $50 \mathrm{~cm} \times 30 \mathrm{~cm} \times 20 \mathrm{~cm}$ that will be required to build a wall whose dimensions are $5 \mathrm{~m} \times 3 \mathrm{~m} \times 2 \mathrm{~m}$ is
(1) 1000
(2) 2000
(3) 3000
(4) 5000

Solution:

(1) 1000