From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2
Solution:
The figure of the solid can be created as per the given information as shown below.
As the conical cavity is of the same height and diameter has been hollowed out, it can be seen that one of the bases of the cylinder is not included in the total surface area of the solid.
TSA of the remaining solid = CSA of the cylindrical part + CSA of conical part + Area of one cylindrical base
Let us find the area of the remaining solid by using formulae;
CSA of the cylinder = 2πrh
Area of the base of the cylinder = πr2, where r and h are radius and height of the cylinder respectively.
CSA of the cone = πrl
Slant height of the cone, l = √[r2 + h2]
where r, h and l are radius, height and slant height of the cone respectively.
Height of the cylinder = Height of the cone = h = 2.4 cm
Diameter of the cylinder = diameter of the cone = d = 1.4 cm
Radius of the cylinder = radius of the cone = r = d / 2 = 1.4 / 2 cm = 0.7 cm
Slant height of the cone, l = √[r2 + h2]
l = √[(0.7 cm)2 + (2.4 cm)2]
= √[0.49 cm2 + 5.76 cm2]
= √[6.25 cm2]
= 2.5 cm
TSA of the remaining solid = CSA of the cylindrical part + CSA of conical part + Area of one cylindrical base
= 2πrh + πrl + πr2
= πr (2h + l + r)
= 22/7 × 0.7 cm × (2 × 2.4 cm + 2.5 cm + 0.7 cm)
= 2.2 cm × 8 cm
= 17.6 cm2
Hence, the total surface area of the remaining solid to the nearest cm2 is 18 cm2.
☛ Check: NCERT Solutions Class 10 Maths Chapter 13
Video Solution:
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm²
NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.1 Question 8
Summary:
If from a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out, the total surface area of the remaining solid to the nearest cm2 is 18 cm2.
☛ Related Questions:
- 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
- A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
- A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
- A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.