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1 year ago

Formula valid for all polygons: P =______________

Mathematics

2 answers:

Sergeeva-Olga [200]1 year ago

8 0

Answer:

perimeter = sum of all sides. this is same for polygons

rect: area l×b. peri = 2(l+b)

Step-by-step explanation:

15+5 = 20

20*2 = 40 cm is the perimeter of the given figure

sergiy2304 [10]1 year ago

4 0

Answer:

P = 40 cm

Step-by-step explanation:

Here,

We can see that the given polygon is a rectangle.
The length and breadth of rectangle is 15 cm and 5 cm.

As we know that the formula of perimeter of rectangle is :

$\longrightarrow{\pmb{\tt{P = 2(L + B)}}}$

P = Perimeter
L = Length
B = Breadth

Substituting all the given values in the formula to find the perimeter of rectangle :

$\begin{gathered} \qquad{\longrightarrow{\sf{P = 2(L + B)}}}\\\\\qquad{\longrightarrow{\sf{P = 2(15 + 5)}}}\\\\\qquad{\longrightarrow{\sf{P = 2(20)}}}\\\\\qquad{\longrightarrow{\sf{P = 2 \times 20}}}\\\\\qquad{\longrightarrow{\sf{P = 40}}}\\ \\ \qquad{\star{\underline{\boxed{\sf{ \red{P = 40 \: cm}}}}}}\end{gathered}$

Hence, the perimeter of rectangle is 40 cm.

$\rule{300}{2.5}$

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Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an

Natasha_Volkova [10]

Answer:

The volume of the solid is 243 $\sqrt{2} \ \pi$

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0 ≤ ρ² ≤ 81

0 ≤ ρ ≤ 9

The intersection that takes place in the sphere and the cone is:

$x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81$

$2(x^2 + y^2) =81$

$x^2 +y^2 = \dfrac{81}{2}$

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

$z = \sqrt{x^2+y^2}$

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; $\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}$

Thus, volume: $V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi$