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Step-by-step explanation:
Unit 9 Section 4 : Surface Area and Volume of 3-D Shapes
In this section we calculate the volume and surface area of 3-D shapes such as cubes, cuboids, prisms and cylinders.
Cube Volume = x³
Surface area = 6x²
Cuboid Volume = xyz
Surface area = 2xy + 2xz + 2yz
Cylinder Volume = π r²h
Area of curved surface = 2π rh
Area of each end = π r²
Total surface area = 2π rh + 2π r²
Prism A prism has a uniform cross-section
Volume = area of cross section × length = A l
Example 1
(a)
Calculate the volume of the cuboid shown.
(b)
Calculate the surface area of the cuboid shown.
Example 2
Calculate the volume and total surface area of the cylinder shown.
Example 3
Calculate the volume of this prism.
Exercises
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Question 1
Calculate the volume and surface area of each of the following cuboids:
(a)
Volume =
cm³
Surface area =
cm²
(b)
Volume =
m³
Surface area =
m²
Question 2
Giving your answers correct to 3 significant figures, calculate the volume and total surface area of each of the following cylinders:
(a)
Volume =
cm³
Surface area =
cm²
(b)
Volume =
cm³
Surface area =
cm²
Question 3
Calculate the volume of each of the following prisms:
(a)
cm³
(b)
m³
Question 4
Calculate the volume and surface area of the following prism:
Volume =
m³
Surface area =
m²
Question 5
The diagram shows a wooden block that has had a hole drilled in it. The diameter of the hole is 2 cm.
Calculate the volume of this solid, giving your answer correct to 2 decimal places.
cm³
Question 6
A concrete beam is to rest on two concrete pillars. The beam is a cuboid with sides of length 0.5m, 3m and 0.4m. The pillars have diameter 0.4m and height 2m. Calculate the total volume of concrete needed to make the beam and the pillars. Round your answer to a sensible level of accuracy.
m³
Question 7
The diagram shows the cross-section of a pipe of length 50 cm.
The inner diameter of the pipe is 20 cm and the outer diameter is 30 cm.
(a)
Calculate the volume of metal needed to make the pipe. Round your answer to a sensible level of accuracy.
cm³
(b)
Calculate the total surface area of the pipe, including the inside surface.
Round your answer to 3 significant figures.
cm²
Question 8
The diagram shows a prism.
The cross-section of the prism consists of a rectangle and a semicircle.
(a)
Calculate the volume of the prism. Give your answer to the nearest cm³.
cm³
(b)
Calculate the total