Each plane surface of a solid is called a face.
The curved surface of a solid is called a lateral surface. Each line of the section of the plane surface is called an edge.
The volume of a solid is the amount of space enclosed within its bounding faces and is measured by the number of cubic units (cubic meter, cubic centimetre, etc.) which it contains.
Results
#1. Find the surface area of a 10 cm * 4 cm * 3 cm brick.
Find the surface area of a 10 cm * 4 cm * 3 cm brick.
Surface area =[ 2(10*4 plus 4*3 plus 10*3)]cm²
=164 cm²
#2. How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
Number of cubes= (100*100*100/10*10*10)
1000
#3. If the volumes of two cubes are in the ratio 27:1, the ratio of their edges is :
If the volumes of two cubes are in the ratio 27:1, the ratio of their edges is :
let their edges be a and b then
a³/b³=27/1
(a/b)³=(3/1)³
a/b=3/1
a : b= 3 : 1
#4. A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out
A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out
volume = Πr²h
= (22/7*1*1*14)m³
=44 m³
#5. The slant height of a right circular is 10 metre and its height is 8 metre. Find the area of its curved surface?
The slant height of a right circular is 10 metre and its height is 8 metre. Find the area of its curved surface?
L=10 m , H= 8 m
r= √ l²-h²
r = √ 10² – 8²
= 6 m
curved surface area = Πrl
= (Π*6*10) m²
=60Πm²
#6. The height of a closed cylinder of given volume and the minimum surface area is :
#7. The slant height of a conical mountain is 2.5 kilometre and the area of its base is 1.54 km sq.The height of mountain is :
The slant height of a conical mountain is 2.5 kilometre and the area of its base is 1.54 km sq.The height of mountain is :
Let the radius of the base be r km
Πr²= 1.54
r²= (1.54* 7/22)
= 0.49
r= 0.7 km
now L=2.5 km, r= 0.7 km,
h= √(2.5)²-(0.7)²
= √(6.25- 0.49) km
=√5.76 km
=2.4 km
#8. If both the radius and height of a right circular cone are increased by 20 %, its volume will be increased by :
If both the radius and height of a right circular cone are increased by 20 %, its volume will be increased by :
Hint : original volume = 1/3 Πr²h
increase%=72.8%
#9. The radii of two cones are in the ratio 2 : 1 there volume are equal. Find the ratio of there height :
The radii of two cones are in the ratio 2 : 1 there volume are equal. Find the ratio of there height :
Let there radii 2x, x and there height be h and H
respectively then 1/ 3 *Π*(2x)²* h
= 1/3 *Π*x²*H
or h/H= 1/4
#10. The volume of the largest right circular cone that can be cut out a cube of edge 7 cm:
The volume of the largest right circular cone that can be cut out a cube of edge 7 cm:
volume of the largest cone = volume of the cane with diameter of base 7 cm and height 7 cm
= (1/3*22/7*3.5*3.5*7) cm³
=(269.5/3)cm³
=89.8 cm³
#11. If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of the sphere is :
If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of the sphere is :
4/3πR³/4πR²
=27
R= 81 cm
#12. A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. The radius of the base of the cone is:
A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. The radius of the base of the cone is:
Let the radius of the cone be R cm
1/3π*R²*75 =2/3π*6*6*6
R²=(2*6*6*6/75)
=(144/25)
(12/5)²
R=12/5
=2.4 cm
#13. The total surface area of a solid hemisphere of diameter 14 cm, is :
The total surface area of a solid hemisphere of diameter 14 cm, is :
Total surface area= 3πR²
= (3*22/7*7*7) cm²
=462 cm²
#14. The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :
The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :
volume = volume of a sphere of radius 1 cm
= (4/3π*1*1*1) cm³
= 4/3π cm³
#15. The volume of a sphere in divided by its surface are the result is 27 cm the radius of sphere is :
The volume of a sphere in divided by its surface are the result is 27 cm the radius of sphere is :
volume = 4/3πr³
= r/3(4πr²)
= r/3* surface area
#16. Find the volume and surface area of a cuboid 16 m long, 14 m board and 7 m high.
Find the volume and surface area of a cuboid 16 m long, 14 m board and 7 m high.
volume =( 16*14*7) m³
= 1568 m³
Surface area = [2(16*14 plus 14*7 plus 16*7)]cm²
(2*434)cm²
868 cm²
#17. The surface of area of a cube is 1734 sq. cm. Find its volume.
The surface of area of a cube is 1734 sq. cm. Find its volume.
Let the edge of the cube be a . then
6a²= 1734
a²=289
a=17
volume a³ = (17)³ cm³
= 4913 cm³
#18. The diagonal of a cube is 6√3 cm. Find its volume and surface area.
Let the edge of the cube be a
√3a = 6√3
a = 6
volume = a³=(6*6*6) cm³
=216 cm³
Surface area = 6a²=(6*6*6) cm²
=216 cm²
#19. If the capacity of a cylindrical tank is 1848 m³ cube and the diameter of its base is 14 m, then find the depth of the tank.
Let the depth of the tank be h metres
π*(7)² * h = 1848
h = ( 1848*7/22*1/7*7)
= 12 m