NCERT Class 8 - Chapter 9: Mensuration
Mensuration is a branch of mathematics that deals with the study of geometric figures and the calculation of their area, perimeter, volume, and surface area. In this chapter, we will extend our knowledge of 2D shapes to understand the properties of 3D shapes.
Cuboid
Total Surface Area (TSA):
\( TSA = 2(lb + bh + hl) \)
\( TSA = 2(lb + bh + hl) \)
Lateral Surface Area (LSA):
\( LSA = 2(l + b)h \)
\( LSA = 2(l + b)h \)
Volume:
\( Volume = l \times b \times h \)
\( Volume = l \times b \times h \)
Figure of a Cuboid with length, breadth and height labeled.
Cube
Total Surface Area (TSA):
\( TSA = 6a^2 \)
\( TSA = 6a^2 \)
Lateral Surface Area (LSA):
\( LSA = 4a^2 \)
\( LSA = 4a^2 \)
Volume:
\( Volume = a^3 \)
\( Volume = a^3 \)
Figure of a Cube with side length 'a' labeled.
Cylinder
Total Surface Area (TSA):
\( TSA = 2 \pi r (r + h) \)
\( TSA = 2 \pi r (r + h) \)
Lateral Surface Area (LSA) (Curved Surface Area):
\( LSA = 2 \pi r h \)
\( LSA = 2 \pi r h \)
Volume:
\( Volume = \pi r^2 h \)
\( Volume = \pi r^2 h \)
Figure of a Cylinder with radius and height labeled.
Cone
Total Surface Area (TSA):
\( TSA = \pi r (l + r) \)
\( TSA = \pi r (l + r) \)
Lateral Surface Area (LSA) (Curved Surface Area):
\( LSA = \pi r l \)
\( LSA = \pi r l \)
Volume:
\( Volume = \frac{1}{3} \pi r^2 h \)
\( Volume = \frac{1}{3} \pi r^2 h \)
Figure of a Cone with radius, height and slant height labeled.
Sphere
Total Surface Area (TSA):
\( TSA = 4 \pi r^2 \)
\( TSA = 4 \pi r^2 \)
Volume:
\( Volume = \frac{4}{3} \pi r^3 \)
\( Volume = \frac{4}{3} \pi r^3 \)
Figure of a Sphere with radius labeled.
Hemisphere
Total Surface Area (TSA):
\( TSA = 3 \pi r^2 \)
\( TSA = 3 \pi r^2 \)
Lateral Surface Area (LSA) (Curved Surface Area):
\( LSA = 2 \pi r^2 \)
\( LSA = 2 \pi r^2 \)
Volume:
\( Volume = \frac{2}{3} \pi r^3 \)
\( Volume = \frac{2}{3} \pi r^3 \)
Figure of a Hemisphere with radius labeled.