Practice questions for Mensurations

Material will be measures by the surface area
Surface Area of Cuboid A= 2(LB + BH+ LH) = 2(23 *30 + 30*40 + 23 *40) =2*2810 cm²
Surface Area of Cuboid B= 2(LB + BH+ LH) = 2(30*12 + 12*44 + 30 *44) =2*2208 cm²
So Cuboid A will require the higher amount of material to make

L = 2+ 2 + 2= 6 cm
B=2 cm
H=2 cm
Surface Area of Cuboid = 2(LB + BH+ LH) = 2(6 *2 + 2*2 + 6 *2) =56 cm²

Surface of cube= 6a²
So , 6a²=2400
a=20 cm

Here L=2 m, B=3 m and H=2.5 m
Total surface area of a cuboid =2LB+2BH+2LH Now is she left bottom and back side of box area covered is =2LB+2BH+2LH-LB-LH = LB+2BH+LH =(2*3)+2(3*2.5)+(2.5*2) = 26m²

Here L=25 m, B=12 m and H=8 m
Area to be painted= Area of lateral surface + Area of Ceiling
=2(LH) + 2(BH) + LB
=892 m²
Theerefore, no of cans required= 892/200
=4.5 cans

here r=14 m and h=3 m
Sheet of metal require = total surface area of Cylinder = 2 π rh + π r²
=880 m²

Here B= 33 cm
Area of Rectangular Sheet formed = Surface Area of the Cylinder
Area of Rectangle = L × B
Therefore
L × B= 4224
Putting the value of B and solving
L=4224/33=128 cm
Now
Perimeter Of Rectangle=2(L+B) = 2(128+33)
=322cm

Length of roller = 1m = 100cm , Diameter of road roller = 154 cm
Circumference of roller = 2 π r= π D = 22/7 * 154 = 484 cm
Now Length travelled in 1 rev= Circumference of road roller
Therefore
Length of road = Length travelled in 750 = 750 * Circumference of road roller = 363,000 cm
Width of road = length of roller = 100 cm
Area of road = Area of rectangle = L * B = 363,000 * 100 = 363 * 10⁵ cm ²

L = 88 cm
B= 20 cm
As per the question,Since cylinder is made out of it, by rolling the foil along width ,the circumference will be equal to the breadth of the sheet and the length will be the height of the cylinder.
Circumference=2 π r= 20 cm
or r= 10/π
Height of the cylinder = 88 cm
Now volume = π r^2 h = 88 *100/π = 2800 cm²

Surface area to be painted = 2(LH+BH) = 2H(L+B)
given perimeter of floor = 250m = 2(L+B)
and height is 4m
Substituting these values
Surface area=1000 m²
cost of painting 1 square metre=Rs 12
cost of painting 1000 square metre=1000*12= Rs 12000

$V_1=L^3$ and $SA_1= 6L^2$
$V_2= (3L)^3 = 27L^3$ and $SA_2=6(3L)^2 = 9 \times 6L^2$
So, Volume becomes 27 times and Surface Area become 9 times

$V= \pi r^2 h$ and $SA= 2 \pi rh$
If radius is doubled and height remains same ,then
$V_2= \pi (2r)^2 h = 4 \pi r^2 h$
$SA_2 = 2 \pi (2r) h =2 \times 2 \pi rh$
So volume becomes four times and Surface area becomes doubled

$V= \pi r^2 h$ and $SA= 2 \pi rh$
if its radius remains same and height is doubled ,then
$V_2= \pi r^2 (2h) = 2 \pi r^2 h$
$SA_2 = 2 \pi r (2h) =2 \times 2 \pi rh$
So volume becomes doubled and Surface area becomes doubled

$2 \pi rh= 660$
$ 2\times (22/7) \times r \times 30 = 660$
r=3.5 cm