Surface Areas and Volumes Class 10 Notes Maths Chapter 13

CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 13 Surface Areas and Volumes. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

CBSE Class 10 Maths Notes Chapter 13 Surface Areas and Volumes

SURFACE AREA AND VOLUME OF COMBINATIONS

Cone on a Cylinder.

r = radius of cone & cylinder;
h ₁ = height of cone
h ₂ = height of cylinder
Total Surface area = Curved surface area of cone + Curved surface area of cylinder + area of circular base
= πrl + 2πrh ₂ +πr ² ;
Slant height, l = \(\sqrt { { r }^{ 2 }+{ { { h }_{ 1 }^{ 2 } } } }\)
Total Volume = Volume of cone + Volume of cylinder
= \(\frac { 1 }{ 3 } { \pi r }^{ 2 }{ h }_{ 1 }+{ \pi r }^{ 2 }{ h }_{ 2 }\)

Cone on a Hemisphere:

h = height of cone;
l = slant height of cone = \(\sqrt { { r }^{ 2 }+{ h }^{ 2 } }\)
r = radius of cone and hemisphere
Total Surface area = Curved surface area of cone + Curved surface area of hemisphere = πrl + 2πr ²
Volume = Volume of cone + Volume of hemisphere = \(\frac { 1 }{ 3 } { \pi r }^{ 2 }h+\frac { 2 }{ 3 } { \pi r }^{ 3 }\)

Conical Cavity in a Cylinder

r = radius of cone and cylinder;
h = height of cylinder and conical cavity;
l = Slant height
Total Surface area = Curved surface area of cylinder + Area of the bottom face of cylinder + Curved surface area of cone = 2πrh + πr ² + πrl
Volume = Volume of cylinder – Volume of cone = \({ \pi r }^{ 2 }h-\frac { 1 }{ 3 } { \pi r }^{ 2 }h=\frac { 2 }{ 3 } { \pi r }^{ 2 }h\)

Cones on Either Side of the Cylinder.

r = radius of cylinder and cone;
h ₁ = height of the cylinder
h ₂ = height of cones
Slant height of cone, l = \(\sqrt { { h }_{ 2 }^{ 2 }+{ r }^{ 2 } }\)
Surface area = Curved surface area of 2 cones + Curved surface area of cylinder = 2πrl + 2πrh ₁
Volume = 2(Volume of cone) + Volume of cylinder = \(\frac { 2 }{ 3 } { \pi r }^{ 2 }{ h }_{ 2 }+{ \pi r }^{ 2 }{ h }_{ 1 }\)

Cylinder with Hemispherical Ends.

r = radius of cylinder and hemispherical ends;
h = height of cylinder
Total surface area= Curved surface area of cylinder + Curved surface area of 2 hemispheres = 2πrh + 4πr ²
Volume = Volume of cylinder + Volume of 2 hemispheres = \({ \pi r }^{ 2 }h+\frac { 4 }{ 3 } { \pi r }^{ 3 }\)

Hemisphere on Cube or Hemispherical Cavity on Cube

a = side of cube;
r = radius of hemisphere.
Surface area = Surface area of cube – Area of hemisphere face + Curved surface area of hemisphere
= 6a ² – πr ² + 2πr ² = 6a ² + πr ²
Volume = Volume of cube + Volume of hemisphere = \({ a }^{ 3 }+\frac { 4 }{ 3 } { \pi r }^{ 3 }\)

Hemispherical Cavity in a Cylinder

r = radius of hemisphere;
h = height of cylinder
Total surface area = Curved surface area of cylinder + Surface area of base + Curved surface area of hemisphere
= 2πrh + πr ² + 2πr ² = 2πrh + 3πr ²
Volume = Volume of cylinder – Volume of hemisphere = \({ \pi r }^{ 2 }h-\frac { 2 }{ 3 } { \pi r }^{ 3 }\)

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