part 1: knowledge & understanding
1. for each statement below, check off either true or false. 1 mark each = 5 marks total
a) the volume of a prism can be calculated by multiplying its base area by its height or depth. true false
b) the surface area of a three - dimensional figure is the sum of the areas of all of its outer faces, measured in square units. true false
c) net area is when we determine the area of the whole shape and minus the part(s) we dont need. true false
d) when applying an area formula, the measurements can be in different units. true false
e) there is always only one way to find the volume of a prism true false
2. for each of the multiple choice questions below, check off the best answer. 1 mark each = 5 marks total
a) the surface area of figure 1 on the left is 64 ft² 96 ft² 48 ft² 32 ft²
b) the volume of figure 1 on the left is 64 ft³ 96 ft³ 48 ft³ 32 ft³
c) the surface area of figure 2 on the left is approximately 603.19 m² 245.04 m² 885.93 m² 81.68 m²
d) the volume of figure 2 on the left is approximately 282.74 m³ 1130.97 m³ 58.43 m³ 229.96 m³
e) the volume of a sphere with a radius of 6 cm is approximately. see the formulas on page 4. 904.78 cm³ 452.39 cm³ 113.10 cm³ 28.27 cm³

Question

Accepted Answer

# 1. True/False Questions
## a)
# Explanation:
## Step1: Volume formula of prism
The formula for the volume of a prism is $V = B\times h$ (where $B$ is the base area and $h$ is the height or depth).
# Answer:
True
## b)
# Explanation:
## Step1: Surface area definition
By definition, the surface area of a 3 - D figure is the sum of the areas of all its outer faces, measured in square units.
# Answer:
True
## c)
# Explanation:
## Step1: Net area concept
Net area is the sum of the areas of the individual faces (or parts) that make up a shape. It is not about subtracting parts we don't need from the area of the whole shape.
# Answer:
False
## d)
# Explanation:
## Step1: Area formula units
When applying an area formula, the measurements must be in the same units. For example, if using $A = l\times w$ (for a rectangle), $l$ and $w$ should have the same unit (e.g., both in meters or both in centimeters).
# Answer:
False
## e)
# Explanation:
## Step1: Volume of prism methods
For example, for a rectangular prism, $V=l\times w\times h$ (where $l$ is length, $w$ is width and $h$ is height) and also $V = B\times h$ (where $B=l\times w$). There can be multiple equivalent ways to calculate the volume of a prism depending on how we express the base area.
# Answer:
False

# 2. Multiple - Choice Questions
## a)
# Explanation:
## Step1: Surface area of a cube formula
The surface area of a cube with side length $s$ is $SA = 6s^{2}$. Given $s = 4$ ft, then $SA=6\times(4)^{2}=6\times16 = 96$ $ft^{2}$.
# Answer:
$96\ ft^{2}$
## b)
# Explanation:
## Step1: Volume of a cube formula
The volume of a cube with side length $s$ is $V=s^{3}$. Given $s = 4$ ft, then $V=(4)^{3}=64$ $ft^{3}$.
# Answer:
$64\ ft^{3}$
## c)
# Explanation:
## Step1: Surface area of a cylinder formula
The surface area of a cylinder is $SA = 2\pi r(r + h)$. Given $r=\frac{6}{2}=3$ m and $h = 10$ m. Then $SA=2\pi\times3\times(3 + 10)=6\pi\times13=78\pi\approx78\times3.14 = 244.92\approx245.04$ $m^{2}$
# Answer:
$245.04\ m^{2}$
## d)
# Explanation:
## Step1: Volume of a cylinder formula
The volume of a cylinder is $V=\pi r^{2}h$. Given $r = 3$ m and $h=10$ m. Then $V=\pi\times(3)^{2}\times10=90\pi\approx90\times 3.14=282.6\approx282.74$ $m^{3}$
# Answer:
$282.74\ m^{3}$
## e)
# Explanation:
## Step1: Volume of a sphere formula
The volume of a sphere is $V=\frac{4}{3}\pi r^{3}$. Given $r = 6$ cm. Then $V=\frac{4}{3}\pi\times(6)^{3}=\frac{4}{3}\pi\times216 = 288\pi\approx288\times1.57 = 452.16\approx452.39$ $cm^{3}$
# Answer:
$452.39\ cm^{3}$

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QUESTION IMAGE

Question

Explanation:

1. True/False Questions

a)

Step1: Volume formula of prism

Step1: Surface area definition

Step1: Net area concept

Answer:

b)