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2 years ago

......help please...... . .

Mathematics

1 answer:

TiliK225 [7]2 years ago

4 0

Answer:

18.66

Step-by-step explanation:

This shape can be split into two rectangles.

the two rectangles can be labeled as Rectangle A, and Rectangle B.

Shape A:

$1.8cm \times 6.4cm = 11.52cm$

Shape B

$3.4cm \times 2.1cm = 7.14cm$

Then, the area of both rectangles can be added to give the area of the shape.

$11.52cm + 7.14cm = 18.66cm$

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Question 7

serg [7]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - a cone with volume 769?3 ft³ , having a height of 15 ft

To calculate - radius of the cone

We know that ,

$\bold{Volume \: of \: cone = \frac{1}{3}\pi \: r {}^{2} h }\\$

substituting the values in the formula stated above ,

$\bold{769.3 = \frac{1}{3} \times 3.14 \times r {}^{2} \times 15} \\ \\\bold{\implies r {}^{2} = \frac{769.3 \times 3}{3.14 \times 15} } \\ \\\bold{\implies r {}^{2} = \cancel\frac{2307.9}{47.1}} \\ \\\bold{ \implies \: r {}^{2} = 49} \\ \\ \bold{\implies \: r = 7 \: ft}$

therefore ,

radius = 7 cm

hope helpful ~

4 0

2 years ago

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