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: What is the formula to find the total surface area?

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 = $B + \tfrac{1}{2}Pl$ (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.

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).

Question

Why do July and August have the same number of days?

Accepted Answer

Because of history: both months were set to 31 days in the Roman calendar (July for Julius Caesar, August later adjusted for Augustus).

Explanation

The modern month lengths come from Roman calendar reforms, not from any astronomical necessity.

Julius Caesar's calendar reform (the Julian calendar, 46 BCE) reorganized the year and fixed many month lengths. The month originally called Quintilis was renamed July in his honor and was given 31 days.
Later, the month Sextilis was renamed August for the emperor Augustus (about 8 BCE). Tradition and later accounts say Augustus adjusted month lengths so that the month named after him would not be shorter than July; as a result August was given 31 days as well. A popular story says a day was taken from February to do this — that part is plausible but historians debate the exact administrative details.

When the Gregorian reform of 1582 adjusted leap-year rules, it did not change month lengths, so July and August remain 31 days today.

Bottom line: July and August both have 31 days because of political/historical decisions in Roman times (honoring Julius and Augustus), not because of any natural or astronomical reason.