Textbook Solutions: Mensuration

 Page 1


Mensuration 
Practice Set 7.1 
Q. 1. Find the volume of a cone if the radius of its base is 1.5 cm and its 
perpendicular height is 5 cm. 
Answer : Radius of base of cone, r = 1.5cm 
Perpendicular height of cone, H = 5cm 
As we know that, 
 
On substituting the given values, 
 
 
 
? V = 11.79 cm
3
 
? Volume of the cone is 11.79 cm
3 
Q. 2. Find the volume of a sphere of diameter 6 cm. 
Answer : Diameter of the sphere, d = 6 cm 
? Radius of sphere, r = 3 cm 
 
 
? V = 113.04 cm
3
 
Page 2


Mensuration 
Practice Set 7.1 
Q. 1. Find the volume of a cone if the radius of its base is 1.5 cm and its 
perpendicular height is 5 cm. 
Answer : Radius of base of cone, r = 1.5cm 
Perpendicular height of cone, H = 5cm 
As we know that, 
 
On substituting the given values, 
 
 
 
? V = 11.79 cm
3
 
? Volume of the cone is 11.79 cm
3 
Q. 2. Find the volume of a sphere of diameter 6 cm. 
Answer : Diameter of the sphere, d = 6 cm 
? Radius of sphere, r = 3 cm 
 
 
? V = 113.04 cm
3
 
? Volume of sphere is 113.04 cm
3 
Q. 3. Find the total surface area of a cylinder if the radius of its base is 5 cm and 
height is 40 cm. 
Answer : Radius of base of cylinder, r = 5 cm 
Height of cylinder, H = 40 cm 
As we know, 
Total surface area of cylinder, A = 2pr (r + h) 
On substituting the values, we get, 
A = 2× (3.14) × 5 × (5 + 40) 
? A = 1413 sq.cm 
? Total surface area of square is 1413 sq. cm 
Q. 4. Find the surface area of a sphere of radius 7 cm. 
Answer : Radius of sphere, r = 7cm 
As we know, the surface area of sphere, A = 4pr
2
 
On substituting the values, we get, 
 
? A = 616 sq. cm 
? Surface area of sphere is 616 sq. cm 
Q. 5. The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone 
of height 24 cm is made. Find the radius of its base. 
Answer : Since the volume of cuboid = length× breadth× height 
? Volume of cuboid = Product of the given three dimensions 
? Volume of cuboid = 44× 21× 12 
Height of cone, H = 24 cm 
Page 3


Mensuration 
Practice Set 7.1 
Q. 1. Find the volume of a cone if the radius of its base is 1.5 cm and its 
perpendicular height is 5 cm. 
Answer : Radius of base of cone, r = 1.5cm 
Perpendicular height of cone, H = 5cm 
As we know that, 
 
On substituting the given values, 
 
 
 
? V = 11.79 cm
3
 
? Volume of the cone is 11.79 cm
3 
Q. 2. Find the volume of a sphere of diameter 6 cm. 
Answer : Diameter of the sphere, d = 6 cm 
? Radius of sphere, r = 3 cm 
 
 
? V = 113.04 cm
3
 
? Volume of sphere is 113.04 cm
3 
Q. 3. Find the total surface area of a cylinder if the radius of its base is 5 cm and 
height is 40 cm. 
Answer : Radius of base of cylinder, r = 5 cm 
Height of cylinder, H = 40 cm 
As we know, 
Total surface area of cylinder, A = 2pr (r + h) 
On substituting the values, we get, 
A = 2× (3.14) × 5 × (5 + 40) 
? A = 1413 sq.cm 
? Total surface area of square is 1413 sq. cm 
Q. 4. Find the surface area of a sphere of radius 7 cm. 
Answer : Radius of sphere, r = 7cm 
As we know, the surface area of sphere, A = 4pr
2
 
On substituting the values, we get, 
 
? A = 616 sq. cm 
? Surface area of sphere is 616 sq. cm 
Q. 5. The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone 
of height 24 cm is made. Find the radius of its base. 
Answer : Since the volume of cuboid = length× breadth× height 
? Volume of cuboid = Product of the given three dimensions 
? Volume of cuboid = 44× 21× 12 
Height of cone, H = 24 cm 
Let Radius of cone be r 
Volume of cone  
As the cone is melted to form a cone, 
? Volume of cone = volume of cuboid 
 
 
 
? r = 21 cm 
? The radius of the cone is 21 cm 
Q. 6. Observe the measures of pots in figure 7.8 and 7.9. How many jugs of water 
can the cylindrical pot hold? 
 
 
Answer : Height of water jug, HJ = 10cm 
 
Radius of water jug, RJ = 3.5 cm 
 
Let the number of jugs be n. 
Page 4


Mensuration 
Practice Set 7.1 
Q. 1. Find the volume of a cone if the radius of its base is 1.5 cm and its 
perpendicular height is 5 cm. 
Answer : Radius of base of cone, r = 1.5cm 
Perpendicular height of cone, H = 5cm 
As we know that, 
 
On substituting the given values, 
 
 
 
? V = 11.79 cm
3
 
? Volume of the cone is 11.79 cm
3 
Q. 2. Find the volume of a sphere of diameter 6 cm. 
Answer : Diameter of the sphere, d = 6 cm 
? Radius of sphere, r = 3 cm 
 
 
? V = 113.04 cm
3
 
? Volume of sphere is 113.04 cm
3 
Q. 3. Find the total surface area of a cylinder if the radius of its base is 5 cm and 
height is 40 cm. 
Answer : Radius of base of cylinder, r = 5 cm 
Height of cylinder, H = 40 cm 
As we know, 
Total surface area of cylinder, A = 2pr (r + h) 
On substituting the values, we get, 
A = 2× (3.14) × 5 × (5 + 40) 
? A = 1413 sq.cm 
? Total surface area of square is 1413 sq. cm 
Q. 4. Find the surface area of a sphere of radius 7 cm. 
Answer : Radius of sphere, r = 7cm 
As we know, the surface area of sphere, A = 4pr
2
 
On substituting the values, we get, 
 
? A = 616 sq. cm 
? Surface area of sphere is 616 sq. cm 
Q. 5. The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone 
of height 24 cm is made. Find the radius of its base. 
Answer : Since the volume of cuboid = length× breadth× height 
? Volume of cuboid = Product of the given three dimensions 
? Volume of cuboid = 44× 21× 12 
Height of cone, H = 24 cm 
Let Radius of cone be r 
Volume of cone  
As the cone is melted to form a cone, 
? Volume of cone = volume of cuboid 
 
 
 
? r = 21 cm 
? The radius of the cone is 21 cm 
Q. 6. Observe the measures of pots in figure 7.8 and 7.9. How many jugs of water 
can the cylindrical pot hold? 
 
 
Answer : Height of water jug, HJ = 10cm 
 
Radius of water jug, RJ = 3.5 cm 
 
Let the number of jugs be n. 
Height of cylindrical pot, HP = 10 cm 
Radius of pot, RP = 7 cm 
 
Since the water is transferred from pot to ‘n’ number of jugs, 
? Volume of pot = n × Volume of jug 
 
On substituting the given values, 
 
? n = 3× 2
2
× 1 
? n = 12 cm 
? The cylindrical pot can hold 12 jugs of water. 
Q. 7. A cylinder and a cone have equal bases. The height of the cylinder is 3 cm 
and the area of its base is 100 cm
2
.The cone is placed upon the cylinder. Volume 
of the solid figure so formed is 500 cm
3
. Find the total height of the figure. 
 
 
Answer : Let the radius of base be r. 
Let the height of cone = H 
Height of cylinder, h = 3cm 
Area of base, A = 100 sq. cm 
Page 5


Mensuration 
Practice Set 7.1 
Q. 1. Find the volume of a cone if the radius of its base is 1.5 cm and its 
perpendicular height is 5 cm. 
Answer : Radius of base of cone, r = 1.5cm 
Perpendicular height of cone, H = 5cm 
As we know that, 
 
On substituting the given values, 
 
 
 
? V = 11.79 cm
3
 
? Volume of the cone is 11.79 cm
3 
Q. 2. Find the volume of a sphere of diameter 6 cm. 
Answer : Diameter of the sphere, d = 6 cm 
? Radius of sphere, r = 3 cm 
 
 
? V = 113.04 cm
3
 
? Volume of sphere is 113.04 cm
3 
Q. 3. Find the total surface area of a cylinder if the radius of its base is 5 cm and 
height is 40 cm. 
Answer : Radius of base of cylinder, r = 5 cm 
Height of cylinder, H = 40 cm 
As we know, 
Total surface area of cylinder, A = 2pr (r + h) 
On substituting the values, we get, 
A = 2× (3.14) × 5 × (5 + 40) 
? A = 1413 sq.cm 
? Total surface area of square is 1413 sq. cm 
Q. 4. Find the surface area of a sphere of radius 7 cm. 
Answer : Radius of sphere, r = 7cm 
As we know, the surface area of sphere, A = 4pr
2
 
On substituting the values, we get, 
 
? A = 616 sq. cm 
? Surface area of sphere is 616 sq. cm 
Q. 5. The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone 
of height 24 cm is made. Find the radius of its base. 
Answer : Since the volume of cuboid = length× breadth× height 
? Volume of cuboid = Product of the given three dimensions 
? Volume of cuboid = 44× 21× 12 
Height of cone, H = 24 cm 
Let Radius of cone be r 
Volume of cone  
As the cone is melted to form a cone, 
? Volume of cone = volume of cuboid 
 
 
 
? r = 21 cm 
? The radius of the cone is 21 cm 
Q. 6. Observe the measures of pots in figure 7.8 and 7.9. How many jugs of water 
can the cylindrical pot hold? 
 
 
Answer : Height of water jug, HJ = 10cm 
 
Radius of water jug, RJ = 3.5 cm 
 
Let the number of jugs be n. 
Height of cylindrical pot, HP = 10 cm 
Radius of pot, RP = 7 cm 
 
Since the water is transferred from pot to ‘n’ number of jugs, 
? Volume of pot = n × Volume of jug 
 
On substituting the given values, 
 
? n = 3× 2
2
× 1 
? n = 12 cm 
? The cylindrical pot can hold 12 jugs of water. 
Q. 7. A cylinder and a cone have equal bases. The height of the cylinder is 3 cm 
and the area of its base is 100 cm
2
.The cone is placed upon the cylinder. Volume 
of the solid figure so formed is 500 cm
3
. Find the total height of the figure. 
 
 
Answer : Let the radius of base be r. 
Let the height of cone = H 
Height of cylinder, h = 3cm 
Area of base, A = 100 sq. cm 
As we know the area of circle is pr
2
 
? pr
2
 = 100 ….. (1) 
Volume of complete solid figure, V = Volume of cone + volume of cylinder 
 
 
It is given that volume of solid figure, V = 500 cubic cm 
On substituting the value of V and pr
2
 from eq (1), we get, 
 
? H = 6 cm 
Total height of figure = h + H = 3 + 6 = 9 cm 
? Total height is 9 cm 
Q. 8. In figure 7.11, a toy made from a hemisphere, a cylinder and a cone is 
shown. Find the total area of the toy. 
 
 
Answer : Radius of circular region, r = 3cm 
Height of Cylinder, H = 40cm 
Height of cone, h = 4cm 
As we know, 
Surface area of hemisphere, AH = 2pr
2
 
Surface area of cylinder, Acy = 2prH