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4 years ago

Consider the series given below.

Mathematics

1 answer:

telo118 [61]4 years ago

6 0

Answer:

n = 8

Step-by-step explanation:

This is a geometric sequence where the sum to n terms is

$S_{n}$ = $\frac{a(r^n-1)}{r-1}$

where a is the first term and r the common ratio

r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3 and a = 2, thus

$\frac{2(3^n-1)}{3-1}$ = 6560

$\frac{2(3^n-1)}{2}$ = 6560 ← cancel the 2

$3^{n}$ - 1 = 6560 (add 1 to both sides )

$3^{n}$ = 6561

note that 6561 = $3^{8}$ , hence

$3^{n}$ = $3^{8}$ ⇒ n = 8

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Step-by-step explanation:

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Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger c

Mademuasel [1]

Answer:

Volume of smaller canister = 763.02 $cm^3$

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Step-by-step explanation:

Given that :

Diameter of Smaller canister = 9 cm

Height of Smaller canister = 12 cm

Larger canister is double the size of smaller one i.e. height and diameter are doubled.

To find:

Volume and surface area of each canister and their comparison.

Solution:

First of all, let us have a look at the formula of volume and surface area of a cylinder.

Volume, $V=\pi r^2h$

Surface Area, $A=2\pi r^2+ 2\pi rh$

where r and h are the radius and height of the cylinder respectively.

Radius is half of diameter.

Radius of smaller canister is given by:

$r_1 = \dfrac{9}{2} = 4.5\ cm$

Height, $h_1 =12\ cm$

Volume, $V_1=\pi (4.5)^2 \times 12 = 763.02\ cm^3$

Surface Area, $A_1 = 2 \pi \times 4.5 ^2 + 2\pi\times 4.5 \times 12 = 466.29 \ cm^2$

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Radius of larger canister is given by:

$r_2 = \dfrac{9}{2} \times 2 = 9 cm$

Height, $h_2 =12\times 2 = 24\ cm$

Volume, $V_2=\pi (9)^2 \times 24 = 6104.16\ cm^3$

Surface Area, $A_2 = 2 \pi \times 9 ^2 + 2\pi\times 9\times 24= 1865.16 \ cm^2$

Comparing the results, we can easily see that:

$V_2 = 8 \times V_1\\A_2 = 4 \times A_1$

i.e. Volume becomes 8 times by doubling the size and surface area becomes 4 times by doubling the size.

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