A slice from a circular pizza of diameter 14 inches is cut in a such a way that each slice of pizza has a central angle of 45°. What is the area of each slice of Pizza(in square inches)?
D = 14
R = D/2 = 14/2 =7
Area of each slice of Pizza =πr² * Θ/360°
= (22/7) * 7 * 7 * (45°/360°)
A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?
378 = 2 * 3 * 3 * 3 * 7
525 = 3 * 5 * 5 * 7
Highest Common Factor(HCF) = 3 * 7 = 21
Size of largest tile = 0.21 m by 0.21 m
Minimum Number of tiles = (3.78 * 5.25) / (0.21 * 0.21) = 450
Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 784 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?
Area = 784 cm²
a = 28 cm
Perimeter of Square = 4 * 28
Circumference of a Circle = 4 * 28 * 22/7
2πr = 4 * 4 * 22
r = 16 * 22 * 7 / 2 * 22 = 56 cm Radius of Circle B = 56/4 = 14 cm Area of Circle = πr² = 22/7 * 14 * 14 = 616 cm²
The area of a rectangle is equal to the area of a square whose diagonal is 12√6 metre. The difference between the length and the breadth of the rectangle is 6 metre. What is the perimeter of rectangle ? (in metre).
d = a√2
12√6 = a√2
a = 12√3 l * b = a² = (12√3)² = 432
l – b = 6 ; l = b + 6
(b + 6)*(b) = 432
b² + 6b – 432 = 0
b = 18; l = 24
2(l + b) = 2(24 + 18) = 84m
The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units.If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.
Length = x; Breadth =y
xy – (x-5)(y+3) = 9
3x – 5y – 6 = 0 —(i)
(x+3)(y+2) – xy = 67
2x + 3y -61 = 0 —(ii)
solving (i) and (ii)
x = 17m ; y = 9m
Height of a cylindrical jar is decreased by 36%. By what percent must the radius be increased, so that there is no change in its volume?
volume of cylindrical jar = πr1²h
volume of cylindrical jar = πr2²(64/100)*h = (16/25)*πr2²h
r2²/r1² = 25/16
r2 /r1 = 5/4
(r2 – r1)/r1 = (5 – 4)/4 * 100 = 25%
The sum of the radius and height of a cylinder is 19m. The total surface area of the cylinder is 1672 m², what is the volume of the cylinder?(in m³)
r + h = 19 m
2πr(r + h) = 1672
r = 1672 * 7/ 2 * 22 * 19 = 14
r = 14 ; h = 5
volume of the cylinder = πr²h = (22/7) * 14 * 14 * 5 = 3080 m³
If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192m². What is the area of original rectangle?
length of rectangle = l m
breadth of rectangle = b m
l * (120/100) * b * (80/100) = 192
1.2l * 0.8b = 192
lb = 192 / 1.2 * 0.8 = 200 m²
The respective ratio of curved surface area and total surface area of a cylinder is 4:5. If the curved surface area of the cylinder is 1232cm², What is the height?
4x = curved surface area = 1232
x = 308
5x = total surface area = 1540
curved surface area = 2πrh
total surface area = 2πr(r + h)
2πr(r + h) = 1540
2πr² + 2πrh = 1540
2πr² = 1540 – 1232
r = 7; h = 28
The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?
Perimeter of square = 2 x Perimeter of rectangle
= 2 * 2 (8+7) = 60 cm.
Side of square = 60/4 = 15 cm = Diameter of semi-circle
Circumference of semi-circle = πd/2 + d
= (22/7) * 2 * 15 + 15 = 38.57 cm
Perimeter of a square and an equilateral triangle is equal. If the diagonal of the square is 10√2 cm, then find the area of equilateral triangle?
Diagonal of a square = a√2 = 10√2
so a = 10, perimeter of square = 4*10 = 40 = 3x (x is the length of each side of triangle)
x = 40/3, so are of equilateral triangle = √3/4*40/3*40/3 = (400√3)/9 cm2
Length of a rectangular field is increased by 10 meters and breadth is decreased by 4 meters, area of the field remains unchanged. If the length decreased by 5 meters and breadth is increased by 7 meters, again the area remains unchanged. Find the length and breadth of the rectangular field.
Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b
If the length of the rectangle is increased by 20%, by what percent should the width be reduced to maintain the same area?
let length = 100 and breadth = 100
now new length = 120 and let breadth = b
so, 100*100 = 120*b
b = 250/3, so % decrease = 100 – 250/3 = 50/3 = 16.67%
A cone whose height is half of its radius is melted to from a hemi-sphere. Find the ratio of the radius of the hemi-sphere to that of cone.
volume will remains constant. So,
V = 1/3*22/7*r2*r/2 (volume of cone) and V = 2/3*22/7*R3 (volume of hemisphere)
So, R/r = 1:4
Find the number of spherical balls of radius 1 cm that can be made from a cylinder of height 8 cm and diameter 14 cm?
(22/7)*7*7*8 = x*(4/3)*(22/7)*13 (x = number of spherical balls)
A rectangle whose sides are in the ratio 6:5 is formed by bending a circular wire of radius 21cm. Find the difference between the length and breadth of the rectangle?
circumference of the wire = 2*(22/7)*21 = 22*6
perimeter of rectangle = 2*11x = 22*6, so x= 6
difference = 36 -30 = 6cm
A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one face of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is 512 cubic cm. find the approximate volume of the cone?
when cone is completely fitted inside the cube, then diameter of cone = side of cube and height of cone = height of cube
so, volume = (1/3)*(22/7)*4*4*8 = 134 (approx)
if the radius of a cylinder is doubled and height is halved, what is the ratio between the new volume and the previous volume?
New volume = (22/7)*4r2*h/2 and old volume = (22/7)*r2*h
so ratio = 2:1
A cone of radius 12 cm and height 5 cm is mounted on a cylinder of radius 12 cm and height 19 cm. Find the total surface area of the figure thus formed?
total surface area = curved surface area of cone + curved surface area of cylinder + base area
= (22/7)*12*13 + (22/7)*12*19 + (22/7)*12*12 = 2376 cm2
A rectangular garden is 30 meter long and 20 meter broad. It has 6 meter wide pavements all around it both on its inside and outside. Find the total area of pavements?
Required area = 42*32 – 18*8 = 1200