General Mathematics: Measurement, Geometry, and Conversions

Comprehensive practice flashcards covering solid geometry (surface area and volume), scale and currency conversions, time conversion, temperature conversion scales, and basic SI vs. Imperial measurement units.

What is the difference between the surface area and the volume of a solid?

Surface Area is the total area of all the faces or surfaces of a solid, whereas Volume is the amount of space inside a solid.

What are the surface area ($SA$) and volume ($V$) formulas for a cube and a rectangular prism?

For a cube: $SA = 6a^2$ and $V = a^3$ (where $a = \text{side}$). For a rectangular prism: $SA = 2(lw + lh + wh)$ and $V = lwh$ (where $l = \text{length}$, $w = \text{width}$, and $h = \text{height}$).

What are the surface area ($SA$) and volume ($V$) formulas for a cylinder and a cone?

For a cylinder: $SA = 2\times\frac{22}{7}\times r^2 + 2\times\frac{22}{7}\times rh$ or $SA = 2\times\frac{22}{7}\times r^2 + 2\times\frac{22}{7}\times rh$ ($SA = 2\times\frac{22}{7}\times r^2 + 2\times\frac{22}{7}\times rh$) written as $SA = 2\times\frac{22}{7}\times r^2 + 2\times\frac{22}{7}\times rh$, specifically $SA = 2\times\frac{22}{7}\times r^2 + 2\times\frac{22}{7}\times rh$ in formula form $SA = 2\times\frac{22}{7}\times r^2 + 2\times\frac{22}{7}\times rh$. More simply: Cylinder $SA = 2\times\frac{22}{7}\times r^2 + 2\times\frac{22}{7}\times rh$ and $V = \frac{22}{7}\times r^2 h$; Cone $SA = \frac{22}{7}\times r^2 + \frac{22}{7}\times rl$ and $V = \frac{1}{3}\times\frac{22}{7}\times r^2 h$ (where $r = \text{radius}$, $h = \text{height}$, and $l = \text{slant height}$).

What are the surface area ($SA$) and volume ($V$) formulas for a sphere, and what is the approximate volume of Earth?

For a sphere: $SA = 4\times\frac{22}{7}\times r^2$ and $V = \frac{4}{3}\times\frac{22}{7}\times r^3$ (where $r = \text{radius}$). The volume of Earth is approximately $1.083 \times 10^{12}\text{ km}^3$.

What real-life applications are associated with cubes/prisms, cylinders, cones, and spheres?

Packaging and boxes (cubes and prisms); paint cans and bottles (cylinders); tents and ice cream cones (cones); and balls and planets (spheres).

What is the definition and formula for scale conversion?

A scale shows the relationship between a measurement on a drawing (map, plan, or model) and the actual measurement. Its formula is $\text{Scale} = \frac{\text{Drawing Length}}{\text{Actual Length}}$.

If a map has a scale of $1 : 50{,}000$ and the distance between two towns on the map is $3.5\text{ cm}$, what is the actual distance?

$\text{Actual Distance} = 3.5\text{ cm} \times 50{,}000 = 175{,}000\text{ cm} = 1.75\text{ km}$.

What formula is used for currency conversion, and what is the converted amount of $\text{₱}5{,}000$ if the exchange rate is $\text{₱}1 = \text{\$}0.018$?

$\text{Converted Amount} = \text{Original Amount} \times \text{Exchange Rate}$. For $\text{₱}5{,}000$: $\text{Converted Amount} = 5{,}000 \times 0.018 = \text{\$}90.00$.

What currencies correspond to the symbols $\text{₱}$, $\text{\$}$, $€$, $¥$, $£$, and $\text{C\$}$?

$\text{₱}$ is Philippine Peso, $\text{\$}$ is US Dollar, $€$ is Euro, $¥$ is Japanese Yen, $£$ is British Pound, and $\text{C\$}$ is Canadian Dollar.

How is $2\text{ hr } 45\text{ min } 30\text{ s}$ converted to seconds?

$(2 \times 3600) + (45 \times 60) + 30 = 7200 + 2700 + 30 = 9{,}930\text{ seconds}$.

What are the formulas for converting Celsius ($^{\circ}\text{C}$) to Fahrenheit ($^{\circ}\text{F}$) and Fahrenheit to Celsius?

Celsius to Fahrenheit: $^{\circ}\text{F} = \frac{9}{5}(^{\circ}\text{C}) + 32$. Fahrenheit to Celsius: $^{\circ}\text{C} = \frac{5}{9}(^{\circ}\text{F} - 32)$.

What are the formulas for converting Celsius ($^{\circ}\text{C}$) to Kelvin ($\text{K}$), Kelvin to Celsius, and Fahrenheit ($^{\circ}\text{F}$) to Kelvin?

Celsius to Kelvin: $\text{K} = {^{\circ}\text{C}} + 273.15$. Kelvin to Celsius: $^{\circ}\text{C} = \text{K} - 273.15$. Fahrenheit to Kelvin: $\text{K} = \frac{5}{9}(^{\circ}\text{F} - 32) + 273.15$.

What are the temperature values for freezing water and boiling water across Celsius, Fahrenheit, and Kelvin?

Water freezes at $0\text{ }^{\circ}\text{C}$, $32\text{ }^{\circ}\text{F}$, and $273.15\text{ K}$. Water boils at $100\text{ }^{\circ}\text{C}$, $212\text{ }^{\circ}\text{F}$, and $373.15\text{ K}$.

What are the reference temperatures for room temperature and absolute zero across Celsius, Fahrenheit, and Kelvin?

Room temperature is $25\text{ }^{\circ}\text{C}$, $77\text{ }^{\circ}\text{F}$, and $298.15\text{ K}$. Absolute zero is $-273.15\text{ }^{\circ}\text{C}$, $-459.67\text{ }^{\circ}\text{F}$, and $0\text{ K}$.

How do you calculate the conversion of $25\text{ }^{\circ}\text{C}$ to Fahrenheit and $98.6\text{ }^{\circ}\text{F}$ to Celsius?

For $25\text{ }^{\circ}\text{C}$: $^{\circ}\text{F} = \frac{9}{5}(25) + 32 = 45 + 32 = 77\text{ }^{\circ}\text{F}$. For $98.6\text{ }^{\circ}\text{F}$: $^{\circ}\text{C} = \frac{5}{9}(98.6 - 32) = \frac{5}{9}(66.6) = 37\text{ }^{\circ}\text{C}$.

In Module 3, what three physical quantities are categorized under Measuring Tools?

Length, mass, and time.

According to Module 3, what is the unit equivalence between meters and feet?

$1\text{ m} = 3.28\text{ ft}$.

What units are paired under Basic Units (SI vs. Imperial) in Module 3?

Meter and foot for length; kilogram and pound for mass; and second for time.

What two Conversion Logic pathways are outlined in Module 3?

Temperature conversion logic: Celsius to Fahrenheit to Kelvin; Liquid volume conversion logic: Liter to Milliliter to Gallon.

What two real-world application fields of basic measurement and conversion are highlighted in Module 3?

Construction and Culinary Arts.