Surface area of composite 3D Figures practice
1) Find the total surface area of a rectangular prism with dimensions: length=10 units, width=5 units and height=6 units.
Solution:
The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh
Substitute the given values:
SA = 2(10)(5) + 2(10)(6) + 2(5)(6)
SA = 100 + 120 + 60
SA = 280 square units
2) Determine the surface area of a cylinder with a height of 8 cm and a base radius of 4 cm.
Solution:
The surface area of a cylinder is given by the formula: SA = 2πr(h + r)
Substitute the given values:
SA = 2π(4)(8 + 4)
SA = 8π(12)
SA = 96π square cm
3) Calculate the total surface area of a square pyramid with a base side length of 6 units and a slant height of 5 units.
Solution:
The surface area of a square pyramid is given by the formula: SA = s^2 + 2sℓ
Substitute the given values:
SA = 6^2 + 2(6)(5)
SA = 36 + 60
SA = 96 square units
4) Find the surface area of a sphere with a radius of 7 cm.
Solution:
The surface area of a sphere is given by the formula: SA = 4πr²
Substitute the given values:
SA = 4π(7)^2
SA = 4π(49)
SA = 196π square cm
5) Calculate the total surface area of a cone with a height of 12 cm and a base radius of 5 cm.
Solution:
Compute the slant height first:
ℓ = sqrt(r^2 + h^2)
ℓ = sqrt(5^2 + 12^2)
ℓ = sqrt(169)
ℓ = 13 cm
Now find the surface area:
SA = πr(r + ℓ)
SA = π(5)(5 + 13)
SA = 5π(18)
SA = 90π square cm
6) A cube has a side length of 10 units. Find the total surface area.
Solution:
The surface area of a cube is given by the formula: SA = 6s²
Substitute the given values:
SA = 6(10)^2
SA = 6(100)
SA = 600 square units