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Mkey [24]
3 years ago
11

The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris

m. Round your answer to the nearest cubic cm.
Mathematics
1 answer:
Georgia [21]3 years ago
5 0

Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)

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Un apostador pierde en su primer juego el 30% de su dinero, en el segundo juego pierde el 50% de lo que perdió; finalmente en el
sergiy2304 [10]

Responder:

26,62

Explicación paso a paso:

Sea x el dinero original que tenía el jugador:

si un jugador pierde en su primer juego el 30% de su dinero, la cantidad perdida será;

= 30/100 \ of \ x\\= 0.3x

Si en el segundo juego pierde el 50% de lo que perdió, entonces la cantidad perdida en el segundo juego será:

= 50/100 \ of \ 0.3x\\= 0.5 \times 0.3x\\= 0.15x

Si en el tercer juego pierde el 40% de todo lo que ha perdido, la cantidad perdida en el tercer juego será:

=\frac{40}{100} \ of \ (0.3x+0.15x) \\= 0.4(0.45x)\\= 0.2025x

Si la cantidad que le queda para seguir apostando es de 37 soles, entonces para calcular la cantidad original que tiene, sumaremos toda la cantidad perdida y la cantidad restante y equipararemos la cantidad original x como se muestra:

0,3x + 0,15x + 0,2025x + 37 = x

0,6525x + 37 = x

x-0,6525x = 37

0,3475x = 37

x = 37 / 0,3475

x = 106,48

La cantidad que tenía originalmente era de 106,48

75% de 106,48

= 75/100 * 106,48

= 0,75 * 106,48

= 79,86

Tomando la diferencia entre su monto original y su 75% será:

= 106.48-79.86\\= 26.62

3 0
2 years ago
Micahdisu please help
skad [1K]

Answer:

1) A - 42°

2) 74°

3) B - 45°

4) B - 66°

Step-by-step explanation:

1) E = D+H

87 = 45 + H

H = 42°

2) 180 - 50 - D

D = 180 - 44 - 62 = 74°

3) F = 105

H = 180-105 = 75

I + H = C + E

I + 75 = 83 + 37

I = 45°

4) D = 180 - (E + F)

D = 180 - (30 + 57) = 93°

93 = A + 27

A = 66°

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