Solving Problems involving Surface Areas of Solid Figures
LET’ STUDY THESE
1. A room is 9.5 m long, 7 m wide and 4.5 m high. Calculate the surface area of the room.
9.5 m
4.5 m
7m
Let’s see the orthographic view of the room.
9.5 m
9.5 m
4.5 m
Front View
4.5 m
Back View
A = lw = (9.5)(4.5)
= 42.75 m2
A = lw = (9.5)(4.5)
= 42.75 m2
7m
7m
4.5 m
Left Side View
A = lw = (7)(4.5)
= 31.5 m2
4.5 m
Right Side View
A = lw = (7)(4.5)
= 31.52
9.5 m
9.5 m
7m
7m
Top View
Bottom View
A = lw = (9.5)(7)
= 66.5 m2
A = lw = (9.5)(7)
= 66.5 m2
Therefore, the total surface are is the sum of areas of the faces of the rectangular prism.
Surface area = (42.75 + 42.75) + (31.5 + 31.5) + (66.5 + 66.5)
= 281.5 m2
In symbols,
SArectangular prism = 2lw + 2lh + 2wh
= 2(9.5)(7) + 2(9.5)(4.5) + 2(7)(4.5)
= 281.5 m2
2. Find the surface area of the cube if its edge measure 7 cm.
7 cm
Note: Cube has 6 faces which is a square.
Surface Area of a Cube = 6 x Area of the Square
SAcube = 6(7)2 = 6(49) = 294 cm2
3. Calculate the surface area of the sphere if its diameter is 12 cm.
Surface Area of a Sphere = 4 x
Radius =
Area of a Circle
diameter 12

 6 cm
2
2
SAsphere = 4r2 = 4(3.14)(6)2 = 452.16 cm2
4. How many square centimeters of materials are needed to make a closed tin can of radius
4 cm and a height of 10 cm?
4 cm
2r
10cm
4 cm
\
Surface area of a Cylinder = (2 x Area of a Circle) + Area of the Body(rectangle)
SAcylinder = 2r2 + 2rh
= 2(3.14)(4)2 + 2(3.14)(4)(10)
= 351.68 cm2
5. Find the surface area of the cone if the radius of its circular base is 5 cm and if the slant
height measures 8 cm.
Slant height (s) = 8 cm
Surface are of the cone = area of circular base + area of the body
SAcone = r2 + rs
= (3.14)(5)2 + (3.14)(5)(8)
= 204.1 cm2
r = 5 cm
KEY CONCEPTS
The surface area of a solid figure is the sum of the areas of all faces of the figure.
The units for surface area are mm2, cm2, dm2, m2, km2,. Etc.
The table below summarizes the formulas in finding the surface area of common
solid/space figure.
Solid Figure
Surface Area
1. Rectangular Prism
SA = 2lw + 2lh + 2wh
h
w
l
SA = 6s2
2. Cube
s
3. Right Regular Pyramid
SA = Area of the Base +
4 x (Area of the triangular face)
4. Right Circular Cone
SA = r2 + rs, s – slant height
Slant height
SA = 4r2
5. Sphere
SA = 2r2 + 2rh
6. Cylinder
height (h)
radius (r)
LET’S PRACTICE
Complete the following tables below.
A. Cube
Edge
8 cm
3.5 m
2 dm
Surface Area
B. Rectangular Prism
Length
3 cm
6m
1.5 dm
Width
5 cm
10 m
0.5 dm
Height
8 cm
14 m
2 dm
Surface Area
C. Square Pyramid
Area of the Base
25 m2
81 cm2
64 dm2
Height of the Triangular
Face
5m
3 cm
8 dm
Surface Area
D. Cylinder
Radius
7 mm
12 cm
10 cm
Height
9 mm
9 cm
12 m
Surface Area
E. Cone
Radius
3.2 dm
8 mm
2 cm
Slant Height
4 dm
11 mm
4 cm
Surface Area
F. Sphere
Radius
4m
2 cm
1.5 dm
Surface Area
ENHANCE YOUR SKILLS
Compute the surface area of the given solid figures
1.
5m
2.
12 mm
12 m
6m
7 mm
3.
5.5 cm
h = 11 m
5.
r=4m
4.
15 dm
APPLY YOUR SKILLS
Solve the following problems below. Show your complete solution.
1. An open cubical rice granary has an edge of 3.2 m. If the external surface is to be painted,
what is the surface area to be painted?
2. The measure of the edge of the box which is a cube is 5 dm. Calculate the surface area of
the box?
3. Find the surface area of the cylinder that is12 m high and has a diameter of 10 m?
4. The radius of the beach volleyball is 4 dm. What is its surface area?
5. A rectangular wooden box is 4.5 m by 2.7 m by 1.5 m. What is the surface area, in square
decimeters, if it is completely painted on all sides?
6. A can of sardines has a radius of 10 cm and a height of 25 cm. How much material was
used in making it?
7. The base of a cone is 22 dm in diameter and a slant height of the curved surface is 14 dm.
What is the surface area?
8. My classroom measures 5 m by 4 m by 4 m. How many liters of paint will be needed to
paint its internal surface if 1 liter of paint covers 28 m2? Hint: 1 L = 1 dm2
9. Angeline wants to cover her 5-cylindrical cans with plastic. If each can is 15 cm high and
its diameter is 10 cm, how much materials are needed to cover all her cans?
10. The surface area of a rectangular prism is 576 cm2. Find its height if the length is 12 cm
and if the width is 8 cm?
11. A glass has a diameter of 8 cm and a height of 11 cm. What is the surface area of the
glass?
12. The area of the base of a square pyramid is 49 dm2. If the height of the triangular face is 8
dm., find its total surface area?
13. A box of soap is 7 cm by 4 cm by 3 cm. Find the surface area of the box.
14. Compute the total surface area of the cube if its edge measures 9 cm.?
15. Which has a greater surface area, cylinder A with radius 5 cm and a height of 7 cm or
cylinder B with radius 7 cm and a height of 5 cm?
CHALLENGE
1. What is the ratio of the surface areas of two of two cylinders if the radius of one is
5 cm and the height is 10 cm and the other cylinder has a radius of 10 cm and a
height of 15 cm?
2. What happens to the surface area of a cube if its edge is tripled?
3. Compute the surface area of the cone below.
h = 12 cm
d = 10 cm