Question

AREA, PERMITER AND VOLUME QUESTIONS.

Answer 1

Answer:

Step-by-step explanation:

(A) The radius of the circle is=1.8m

Then  diameter will be: 2r=$2{\times}1.8=3.6 m$

Circumference of circle= ${\pi}d$=$3.14{\times}3.6=11.304 m$

Area of the circle=${\pi}r^{2}=3.14{\times}(1.8)^{2}=10.17 m^{2}$

(B) The area of the rectangular backboard of basketball court = 18900$cm^{2}$

Width=180cm

Area of rectangle= l{\times}b[/tex]

18900=l{\times}180[/tex]

$l=105 cm=1.05m$

Perimeter of the seating space=2(l+b)

=$2(32.5+18.4)$

=$101.8 m$

Perimeter of the basketball court=2(l+b)

=$2(15+28)$

=$86 m$

Now, total perimeter= perimeter of the basketball court+perimeter of the seating space.

Total perimeter=$101.8+86=187.8 m$

Area of the seating space=$l{\times}b$

=$32.5{\times}18.4=598 m^{2}$

(C) The shape consists of one square and 4 triangles, therefore area of square= $(side)^{2}=(3)^{2}=9 m^{2}$

Area of 4 triangles=$4{\times}(\frac{1}{2}{\times}B{\times}H)$

=$4{\times}(\frac{1}{2}{\times}3{\times}2)=12m^{2}$

Area of the shape= Area of the square+ area of the 4 triangles

=$9+12=21m^{2}$

(D) Perimeter of rectangle with length=40 m (After converting cm to m) and breadth= 10 m is given by: $2(l+b)=2(40+10)=100 m$

Perimeter of rectangle with length 68 m and breadth=33 m is given by:$2(l+b)=2(68+33)=202 m$

Perimeter of  the semicircle=$\frac{{\pi}d}{2}=\frac{3.14{\times}34}{2}=53.38 m$

Total perimeter= $100+201+53.38=355.38 m$

Area of rectangle with length=40 m (After converting cm to m) and breadth= 10 m is given by:$l{\times}b=40{\times}10=400 m^{2}$

Area of rectangle with length 68 m and breadth=33 m is given by:$l{\times}b=68{\times}33=2244 m^{2}$

Area of the semi circle=$\frac{{\pi}r^{2}}{2}=\frac{3.14{\times}17^{2}}{2}=453.73 m^{2}$

Total  area= $400+2244+453.73=3097.73 m^{2}$

Answer 2

Answer:

1.

Part 1: Circumference is 11.31 meters

Part 2: Area is 10.18 square meters

2.

Part 1: Backboard's Length = 1.05 meters

Part 2: Perimeter is 187.8 meters

Part 3: Area of seating space is 178 square meters

3. Area is 21 square meters.

4.

Part 1: Perimeter is 255.41 meters

Part 2: Area is 3097.97 square meters.

Step-by-step explanation:

Question 1:

Part 1:

The formula for the circumference of a circle is given by:

$C=\pi d\\C=\pi (2r)\\C=2\pi r$

Where radius (r) is half of diameter (d)

Since radius of the circle shown in 1.8m, we plug it in the formula and get:

$C=2\pi r\\C=2\pi (1.8)\\C=11.31$

So C = 11.31 meters

Part 2:

The area of the circle is given by the formula:

$A=\pi r^2$

Where A is the area and r is the radius

Since we know r = 1.8, we plug it in the formula and find area:

$A=\pi r^2\\A=\pi(1.8)^2\\A=10.18$

Area is 10.18 sq. meters.

Question 2:

Part 1:

Area of a rectangle is length * width

width is given in 1.8 m, which in cm, is 1.8 multiplied by 100, so we have

$1.8*100=180$cm

To find Length, we plug area equal to 18,900 and width equal to 180 cm and solve:

$A=length*width\\18,900=length*180\\length=\frac{18,900}{180}\\length=105$

Length is 105 cm, in meters, we divide by 100, to get $\frac{105}{100}=1.05$

Backboard's Length = 1.05 meters

Part 2:

Perimeter means the sum of all the sides of the figure (however many sides it might have). If you look at the seating space, it has 8 sides, 4 of the outer sides and 4 of the inner sides. We just add all of them to get the perimeter.

Perimeter = $18.4+32.5+18.4+32.5+15+28+15+28=187.8$

Thus the perimeter is 187.8 meters

Part 3:

Area of the seating space can be written as:

Area of seating space = area of big rectangle - area of basketball court

Area of big rectangle is length * width = $18.4*32.5=598$

Area of basket ball court is length * width = $15*28=420$

Now,

Area of seating space = 598 - 420 = 178 square meters.

Question 3:

Area shape consists of 4 same triangles (with base of 3 and height of 2) & 1 square (with side 3) in the middle.

To get the area of the shape we add area of 4 triangles & area of square.

Area of 1 triangle is

$A=\frac{1}{2}*b*h=\frac{1}{2}*3*2=3$

Area of 4 of the triangles is

$4*3=12$

Now, area of square is given by (side * side):

$A=s^2=3^2=9$

Area of square is 9

Hence, area of shape = 12+9=21 square meters

Question 4:

Part 1:

The perimeter is sum of all the sides of the figure. If we start from left side (4000cm) and go clockwise, we can identify all the sides.

• Starting side is 4000 cm side. 4000cm divided by 100 (to get it into meters): 40 m
• top is 10 m and 68 m = 78 m
• right side is 33 m
• then we have semicircle, since whole circle's circumference (perimeter) is $2\pi r$, semicircle's perimeter is half of that so  $\frac{2\pi r}{2}=\pi r=\pi (17)=53.41$m
• then a side of 34 m (bottom)
• then 700 cm , in meters we divide by 100, so 7m
• then 10 m is the last one before we come to starting point

Perimeter = $40+10+68+33+53.41+34+7+10=255.41$

Perimeter is 255.41 meters

Part 2:

Area of the figure can be found by dividing the figures. From left, we can see that the whole figure consists of

• Left rectangle with length 40 m and width 10 m. Thus area of rectangle is length * width = 40 * 10 = 400
• Then another rectangle with length 68 m and width 33 m. Thus area of this rectangle is length * width = 68 * 33 = 2244
• Lastly in the bottom we have half a circle, area of whole circle is $\pi r^2$ and that of this semicircle is half of this so area is $\frac{\pi r^2}{2}=\frac{\pi (17)^2}{2}=453.96$

Adding all these we get the area of the figure:

Area = $400+2244+453.96=3097.96$

Area is 3097.97 square meters.