Practice Set 7.1 Mensuration Class 10th Mathematics Part 2 MHB Solution

Practice Set 7.1
  1. Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular…
  2. Find the volume of a sphere of diameter 6 cm.
  3. Find the total surface area of a cylinder if the radius of its base is 5 cm and height…
  4. Find the surface area of a sphere of radius 7 cm.
  5. The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height…
  6. Observe the measures of pots in figure 7.8 and 7.9. How many jugs of water can the…
  7. A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area…
  8. In figure 7.11, a toy made from a hemisphere, a cylinder and a cone is shown. Find the…
  9. In the figure 7.12, a cylindrical wrapper of flat tablets is shown. The radius of a…
  10. Figure 7.13 shows a toy. Its lower part is a hemisphere and the upper part is a cone.…
  11. Find the surface area and the volume of a beach ball shown in the figure.…
  12. As shown in the figure, a cylindrical glass contains water. A metal sphere of diameter…
Practice Set 7.1
Question 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,


Volume of the cone, 


On substituting the given values,










⇒ V = 11.79 cm3


∴ Volume of the cone is 11.79 cm3


Question 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


As we know, the volume of sphere, 



⇒ V = 113.04 cm3


∴ Volume of sphere is 113.04 cm3



Question 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 = 2πr (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



Question 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 = 4πr2


On substituting the values, we get,



⇒ A = 616 sq. cm


∴ Surface area of sphere is 616 sq. cm



Question 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








r2 = 21× 7 × 3


r2 = 21× 21

⇒ r = 21 cm


∴ The radius of the cone is 21 cm


Question 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


Volume of conical jug, 


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× 22× 1


⇒ n = 12 cm


∴ The cylindrical pot can hold 12 jugs of water.



Question 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 cm2.The cone is placed upon the cylinder. Volume of the solid figure so formed is 500 cm3. 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 πr2


⇒ πr2 = 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 πr2 from eq (1), we get,



⇒ H = 6 cm


Total height of figure = h + H = 3 + 6 = 9 cm


∴ total height is 9 cm



Question 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 = 2πr2


Surface area of cylinder, Acy = 2πrH


Surface area of cone is,




ACO = 5πr


Total area = AH + ACY + ACO


On substituting the values, we get,


⇒ Total area = πr(2r + 2H + 5)


⇒ Total area = π× 3× (6 + 80 + 5)


⇒ Total area = 273π


∴ total area of the figure is 273π sq. cm



Question 9.

In the figure 7.12, a cylindrical wrapper of flat tablets is shown. The radius of a tablet is 7 mm and its thickness is 5 mm. How many such tablets are wrapped in the wrapper?



Answer:

Since there are only flat tablets which are stacked onto each other inside the cylindrical wrapper, so the radius of the wrapper does not matter.

Height of wrapper, H = 10cm = 100mm


Thickness of the tablet, h = 5mm



⇒ Number of the tablets = 20


∴ There are 20 tablets inside the cylindrical wrapper.



Question 10.

Figure 7.13 shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and the surface area of the toy from the measures shown in the figure.(π= 3.14)



Answer:

Radius of the circular base, r = 3cm

Height of cone, h = 4cm






⇒ V =3.14×3 × 10


⇒ V = 94.20 cubic cm


Now,




⇒ SC = 3.14 × 3 × 5


⇒ SC = 47.1 sq.cm


Surface area of sphere, SS = 2πr2


⇒ SS = 2× (3.14) × 32


⇒ SS = 56.52 sq.cm


Surface area of toy = 47.1 + 56.52 = 103.52 sq.cm


∴ Volume and surface area of toy is 94.20 cm3 and 103.52 cm2 respectively



Question 11.

Find the surface area and the volume of a beach ball shown in the figure.



Answer:

Diameter of spherical ball, d = 42 cm


Radius of ball, r =21 cm


As we know that, Surface area of sphere, A = 4πr2


⇒ A = 4× (3.14) × (21)2


⇒ A = 5538.96 sq.cm


Also,




⇒ V = 38772.72 cm3


∴ The surface area and volume of the spherical ball is 5538.96 cm2 and 38772.72 cm3 respectively



Question 12.

As shown in the figure, a cylindrical glass contains water. A metal sphere of diameter 2 cm is immersed in it. Find the volume of the water.



Answer:

Diameter of glass, D = 14 cm


⇒ Radius of glass, r = 7cm


Height of water level, H = 30 cm


We know that, volume of cylinder, V = πR2H


⇒ V = π × (7)2× 30


⇒ V = 1470π cubic cm


Diameter pof metal sphere, d = 2 cm


Radius of metal sphere, r = 1cm


As we know that,




⇒ v = 1.33π cubic cm


Volume of water = Volume of glass – Volume of metal sphere


⇒ Volume of water = 1470π – 1.33π


∴ volume of the water is 1468.67π cm3


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