Q: what is standard form of 3x3x3x3

The correct answer is: $81$ Explanation This is repeated multiplication of 3 four times, which can be written using an exponent as $3^4$. Calculate step by step: Steps: First step: $$3\times3=9$$ Second step: $$9\times3=27$$ Final step: $$27\times3=81$$ Therefore, $3^4 = 81$.

Q: 30% of 900

The correct answer is: $270$ Explanation Thirty percent means thirty per hundred, so 30% of a number equals 0.3 times that number. Multiplying 0.3 by 900 gives the result. Steps: First step: $$30\% = \frac{30}{100} = 0.3$$ Second step: $$0.3 \times 900 = 270$$ Final step: $$\text{Therefore, }30\%\text{ of }900\text{ is }270.$$ Therefore, 30% of 900 is 270.

Q: What is 5 over 6 divided by 8?

The correct answer is: $\frac{5}{48}$ Explanation You divide by 8 by multiplying by its reciprocal (1/8). That gives a product of two fractions which you multiply across numerator and denominator. Steps: First step: $$\frac{5}{6}\div 8 = \frac{5}{6}\times\frac{1}{8}$$ Second step: $$\frac{5\times1}{6\times8} = \frac{5}{48}$$ Final step: $$\frac{5}{48}\text{ (cannot be simplified further)}$$ Therefore, $ \frac{5}{6} $ divided by $ 8 $ equals $ \frac{5}{48} $ (approximately $0.1041667$).

Q: Why is the value of k taken as 9×10

The short answer: Because $k$ is Coulomb's constant, defined by $k=\dfrac{1}{4\pi\varepsilon_0}$, and using the measured permittivity of free space gives $k\approx8.99\times10^9$, which is rounded to $9\times10^9$ for simplicity. Explanation Coulomb's law for the electrostatic force between two point charges is usually written as $$F=k\frac{q_1q_2}{r^2}.$$ The constant $k$ is related to the permittivity of free space $\varepsilon_0$ by $$k=\frac{1}{4\pi\varepsilon_0}.$$ The measured value of the vacuum permittivity is $\varepsilon_0\approx8.854187817\times10^{-12}\text{ F/m}.$ Plugging this into the formula gives $$k=\frac{1}{4\pi(8.854187817\times10^{-12})}\approx8.98755179\times10^9\text{ N·m}^2\text{/C}^2.$$ For most textbook and classroom work this is rounded to a convenient value: $$k\approx9\times10^9\text{ N·m}^2\text{/C}^2.$$ The rounding makes calculations easier and the small difference (about 0.14%) is negligible in typical problems. Why that particular number? The numerical value comes from the chosen SI units (meter, kilogram, second, ampere) and the experimentally measured $\varepsilon_0$. Conceptually, $\varepsilon_0$ and hence $k$ arise from the way the electric field behaves in free space (Maxwell’s equations). The value is not arbitrary — it is determined by measurements and the SI system. If you’d like, I can show the numeric substitution step-by-step or explain how the value connects to other constants (e.g., the speed of light and magnetic constant).

Q: When do we use R constant as 0.0821 and 8.

Use R = 0.0821 when pressure is in atmospheres and volume in liters; use R = 8.314 when you work in SI/energy units (pressure in Pa or kPa and volume in m³, or when R must be in joules). Explanation The gas constant appears in the ideal gas law $PV = nRT$. You must choose the R value whose units match the units of $P$ and $V$ you use. Common forms: $R = 0.082057\ \text{L·atm·mol}^{-1}\text{·K}^{-1}$ (often rounded to 0.0821) — use if $P$ is in atm and $V$ is in L. $R = 8.314462\ \text{J·mol}^{-1}\text{·K}^{-1}$ (often rounded to 8.314 or 8.31) — use if you need energy units (J) or if $P$ is in Pa and $V$ in m³ (SI). Other forms: $R = 8.314\ \text{kPa·L·mol}^{-1}\text{·K}^{-1}$ or $0.08314\ \text{bar·L·mol}^{-1}\text{·K}^{-1}$, etc. You can convert between them because they are the same constant expressed with different unit combinations:$$8.314\text{ J·mol}^{-1}\text{·K}^{-1}=8.314\text{ kPa·L·mol}^{-1}\text{·K}^{-1}=0.082057\text{ L·atm·mol}^{-1}\text{·K}^{-1}.$$ Quick rule of thumb Use 0.0821 when PV is in (atm·L). Use 8.314 when PV is in (J) or when P is in Pa (or kPa) and V in m³ (or convert to kPa·L). Always keep units consistent; otherwise your numeric answer will be wrong. Short example Find n from $PV = nRT$ with $P=2.00\ \text{atm}$, $V=10.0\ \text{L}$, $T=300\ \text{K}$:$$n=\frac{PV}{RT}=\frac{2.00\times10.0}{0.0821\times300}\approx0.81\ \text{mol}.$$

Question

What is the formula to find the total surface area?

Accepted Answer

The formula depends on the 3D shape. Here are the total surface area (TSA) formulas for common solids:

Cube: TSA = $6a^2$ (where $a$ is the edge length)  
Rectangular prism (box): TSA = $2(ab + bc + ac)$ (edges $a,b,c$)  
Sphere: TSA = $4\pi r^2$ (radius $r$)  
Right circular cylinder: TSA = $2\pi r^2 + 2\pi r h$ (two circular bases plus curved surface; radius $r$, height $h$)  
Right circular cone: TSA = $\pi r^2 + \pi r l$ (base area $+\,$lateral area; $r$ = base radius, $l$ = slant height)  
Right prism (general): TSA = $2B + Ph$ (where $B$ = area of one base, $P$ = perimeter of the base, $h$ = prism height)  
Pyramid (regular or not): TSA = $B + 	frac{1}{2}Pl$ (base area $B$, perimeter of base $P$, slant height $l$)  
Hemisphere: curved surface = $2\pi r^2$; including base (flat face) TSA = $3\pi r^2$.

If you meant a specific solid, tell me which one and I’ll show a worked example.