The total surface area of a hemisphere of diameter 14cm is
Radius=7cm
Total surface area=3πr²
3πr²=3*22/7*7*7=462
If the volume of a sphere is divided by its surface area,the result is 27cm.Radius of the sphere is
Volume=4/3∏r³
Surface area=4∏r²
Volume/Surface Area=1/3r=27
r=81
The volumes of two spheres are in the ratio 64:27.The ratio of their surface area is
Volume of 1st sphere=4/3()
Volume of 2nd sphere=4/3()
Ratio=(4/3∏r1³)/(4/3∏r2³)=64/27 r1/r2=4/3
Ratio of surface area=4∏r1²/4∏r2²=16:9
The surface area of a sphere is 2464.If its radius be doubled, surface area of new sphere is
Surface area=4πr²=2464
4*22/7*r²=2464,r²=196 ,r=14
New radius=28
Surface area=4π=4*22/7*28*28=9856
Find the volume of a hemisphere whose radius is 21cm.
Radius=21
Volume=2/3(∏r³)=2/3*22/7*21*21*21=19404
The curved surface area of two spheres are in the ratio 1:4.Find ratio of their volumes.
Ratio =1:4
Ratio of radii=1:2
Ratio of volume=4/3(∏r1³)/(4/3*∏r2³)=r1³/r2³=1/8=1:8
Spheres A and B have their radii 40cm and 10cm respectively.The ratio of surface area of A to the surface area of B is
Surface area of 1st sphere=4πr1²
Surface area of 2nd sphere=4πr2²
Ratio=4πr1²/4πr2²=r1²/r2²=16/1=16:1
Find the volume of a sphere whose radius is 7cm.
Radius=14
Volume=4/3(∏r³)=4/3*(22/7*7*7*7)
Volume=1437.33
Find the volume and surface area of a sphere of diameter 42cm.
Volume=4/3(∏r³)=4/3*(22/7*21*21*21)=38808
Surface Area=4=4*(22/7*21*21)=5544
The difference between the circumference and radius of a circle is 74cm.Find area of the circle.
2 π*r- r=r(2 π-1)=74
Solving we get r=14
Area= π*r*r=22/7*14*14=616
A circle and a rectangle have the same perimeter.The sides of the rectangle are 40cm and 26cm.What is the area of the circle?
Perimeter of rectangle=2(40+26)=2*66=132
Circumference=2*22/7*r=132,r=21
Area= π*r*r=22/7*21*21=1386
The length of a rectangle is twice the diameter circle.The circumference of the circle is equal to area of a square of side 22cm.What is the breadth of rectangle if its perimeter is 668cm?
Side of square=22cm
Area=22*22=484
Circumference=2 π*r=484=2*22/7*r=484
R=77 diameter=154 ,length of rectangle=2*154=308
Perimeter=668 ,2*breadth=668-(2*308)=668-616=52 ,breadth=26
The number of revolutions of wheel of diameter 70cm makes in travelling a distance of 990m is
Radius=35
Circumference=2*22/7*35=220
No of revolutions in making 220cm=1
No of revolutions in making 990m=(990*100)/220=450
The circumference of two circles is 88m and 220m respectively.What is the difference between the area of larger circle and smaller circle?
Circumference =88m
2 π*r=2*22/7*r=88
r=14
Circumference =220m
2 π*R=2*22/7*R=220
R=35
Difference=∏R²-∏r²=3234sq.cm
What is the area of a circle whose circumference is 132cm?
Circumference=2*π*r=132
2*(22/7)*r=132
r=21
Area= π*r*r=22/7*21*21=1386sq.cm
The area of a circle of radius 7 is numerically what percent of its circumference?
Area=∏r²=22/7*7*7=154
Circumference=2*22/7*7=44
Percent=(154*100)/44=350%
The radius of a circular wheel is 7/4m.How many revolutions will it make in travelling 11km?
Circumference=2*(22/7)*(7/4)=11m
No of revolutions in making 11m=1
No of revolutions in making 11km=11000/11=1000 revolutions
Find the radius of a circular field whose circumference measures 11/2km
Circumference=2* π*r
11/2=2*22/7*r=7/8km or 7000/8=875m
Areas of two circles are in the ratio 25:64.Find ratio of their radii?
Area of circle1=πr1²
Area of circle2= πr2²
Ratio=25/64=
r1/r2=5/8
Find the circumference of a circle whose radius is 42m
Circumference=2*22/7*42=264
The length of two diagonals of a rhombus is 10cm and 20cm,find its area.
Area=1/2*(d1*d2)
½*(10*20)=100
One side of a parallelogram is 18cm and the distance from opposite side is 8cm.Area of parallelogram is
Area=One side*Height
Area=18*8=144
The base of a parallelogram is twice its height.If the area of the parallelogram is 72sq.cm,find height.
Let height be x,base =2x
B*h=Area
X*2x=72
2=72,
X=6
One diagonal of a parallelogram is 70cm and the perpendicular distance of this diagonal from either of the outlying vertices is 27cm.The area of the parallelogram is
Area=One diagonal*Perpendicular distance
Area=70*27=1890
A parallelogram has sides 30m and length 14m and one of its diagonals is 40m long.Then,find its area.
Area of parallelogram=2*Area of triangle
Area of triangle=
S=1/2(30+14+40)
S=42
Area=√s(s-a)(s-b)(s-c)=168
Area of parallelogram=2*168=336
If diagonals of a rhombus are 5cm and 12cm,find the length of its side?
Side=1/2*√5²+12²
1/2=1/2*13=6.5cm
Each side of a rhombus is 26cm and one of its diagonals is 48cm long.The area of the rhombus is
Second diagonal d2=2*√a²-(d/2)²
Second diagonal d2=2*√26²-(48/2)²
d2=20
Area=1/2(d1*d2)=1/2(48*20)=480
One of the diagonals of a rhombus is double the other diagonal.Its area is 25.Sum of diagonals is
Area=1/2(d1*d2)
25=1/2(d1*2d1)
50=2,25,d1=5
Other diagonal d2=10
Sum=15
The area of a rhombus is 150.The length of one of its diagonals is 10cm.Length of other diagonal is
150=1/2(10*d2)
300=10*d2 , d2=30cm
Find the area of a rhombus one side of which measures 20cm and one diagonal 24cm.
Area of a rhombus=diagonal*√side²-(diagonal/2)²
Area=24* √20²-(24/2)² =24*16=384