Chapter 11: Surface Areas & Volumes

Solution:
The volume (V) of a cuboid is given by the formula: $V = l \times b \times h$.

Solution:
A cube has 6 equal square faces. The area of one face is $a^2$.
The total surface area (TSA) is $6a^2$.

Solution:
Volume of a cube = $side^3 = 5^3 = 125$ cm$^3$.

Solution:
The curved surface area (CSA) of a cylinder is given by the formula: $CSA = 2\pi rh$.

Solution:
Curved surface area is the area of the rectangular surface that forms the body of the cylinder. Total surface area includes the curved surface area plus the area of the two circular bases (top and bottom). TSA = $2\pi rh + 2\pi r^2$.

Solution:
Volume of a cylinder = $\pi r^2 h = \frac{22}{7} \times 7^2 \times 10 = 22 \times 7 \times 10 = 1540$ cm$^3$.

Solution:
The volume of a cone is one-third the volume of a cylinder with the same base and height. $V = \frac{1}{3}\pi r^2 h$.

Solution:
Surface Area of a sphere = $4\pi r^2 = 4 \times \frac{22}{7} \times 7^2 = 4 \times 22 \times 7 = 616$ cm$^2$.

Solution:
A hemisphere is exactly half of a sphere. Its volume is half the volume of a sphere. Volume of hemisphere = $\frac{2}{3}\pi r^3$.

Solution:
Volume of a sphere = $\frac{4}{3}\pi r^3 = \frac{4}{3} \times \pi \times 3^3 = 36\pi$ cm$^3$.