Answer: Option B. -> 110
:
B
Let 6x and 5x be the sides of a rectangle.
$\Rightarrow 6x\times 5x=750$
$\Rightarrow 30x^2=750$
$\Rightarrow x^2=\frac{750}{30}=25$
$\Rightarrow x=5$
Length = 6x = 30m
Breadth = 5x = 25m
Perimeter = 2(l + b) = 2(30 + 25) = 110m

Answer: Option A. -> Rs. 105
:
A
Let n be thenumber of mats required
base of mat = 3 cm
height of mat = 4 cm
Area of the parallelogram= base $\times$height
Area of hall = Area of mat $\times$ number of mats
$\Rightarrow$ 180 = 4 x 3 x n
$\Rightarrow n=\frac{180}{12}=15$
Given that eachmat costs Rs. 7
Then the cost of 15 mats costs = 7 x 15 = Rs.105

Answer: Option A. -> True
:
A
Edge of the cube (a) = 2.5 m
Area of four walls = 4a²
= 4 x 2.5 x 2.5 m²= 25 m²

Answer: Option B. -> False
:
B
Area of the rectangular playground = length × breadth
= 60 × 25 = 1500 m².

Answer: Option A. -> True
:
A

The perimeter of the figure given above is the sum of arc length BC + length AB + length AC.
Perimeter of the given shape = πr + 2 + 2 = [$\frac{22}{7}$ × $\frac{3.5}{2}$ ] + 4
= 5.5 + 4 = 9.5 cm
Hence, it is true.

Answer: Option C. -> 250
:
C
We can calculate the area of this quadrilateral as the sum of the areas of two triangles taking diagonal length 25m as the base for both triangles and perpendicular length 8m as theheight of one triangle and the perpendicular length 12m as theheight of another triangle.

Area of triangle = $\frac{1}{2}\times base\times height$
Area of the first triangle = $\frac{1}{2}\times 25\times 8$
Area of the second triangle = $\frac{1}{2}\times 25\times 12$
Area of quadrilateral =Area of the first triangle +Area of the second triangle
Area of quadrilateral = $\frac{1}{2}\left(25\right)(8+12)=250m^2$

Answer: Option C. -> 286 cm2
:
C
The metal sheet is in the shape of a cuboid.
Total surface area of the cuboid is given by2 (lb + bh + hl) = 2[(27 ×8) + (8 ×1) + (1 ×27)] = 502 $c{m}^2$.
When themetal sheet is melted into a cube, then the volume of themetal sheet will be equal to the volume of thecube.
Hence, Volume of the cuboid = Volume of the cube
Let eachside of thecube be $a$
Hence, 27 × 8 × 1 = $a^3$
⇒$a$ = 6 cm
Total Surface area of the cube is given by$6a^2$ = 6 × (6)² = 216 $c{m}^2$.
Hence, the difference between surface areas of two solids = (502 -216)$c{m}^2$ = 286 $c{m}^2$.

Answer: Option A. -> 144 cm3
:
A
Let the dimension of a cuboid be l, b, and h.
Since the six surface areas are given:
$\Rightarrow$ l $\times$b = 12.......................................(1)
$\Rightarrow$ b$\times$h=36.......................................(2)
$\Rightarrow$ l $\times$h= 48.......................................(3)
Now multiplying equation (1),(2) and (3), we get
$\Rightarrow (l\times b)\times (b\times h)\times \left)\right(l\times h)=12\times 36\times 48$
$\Rightarrow$ $(l\times b\times h{)}^2=20736$
$\Rightarrow (l\times b\times h)=\sqrt{20736}=144c{m}^3$
Since volume of a cuboid is calculated as ${}^{\prime }l\times b\times h^{\prime }$, the required volume is$144c{m}^3$.

Answer: Option C. -> πr2h
:
C
A soda can is a rough example of a cylinder.
The volume of acylinder is $\pi r^{2}h$.
The capacity of any vessel is its internal volume so, the capacity of asoda canbe calculated using the formula $\pi r^{2}h$.
Where,
r = base radius of the can
h = height of the can

Answer: Option B. -> False
:
B
Volume of cube=${\left(edge\right)}^3$
Hence the volume of cube with edge 24 m is ${\left(24\right)}^3$
= 13824 $m^3$.