What is the sum of the arithmetic sequence 6, 14, 22, if there are 26 terms

1 answer:

3 0

Sum of nth term of arithmetic sequence is given by Sn = n/2[2a + (n - 1)d]
Here, a = 6, n = 26 and d = 14 - 6 = 8
S26 = 26/2[2(6) + (26 - 1)8] = 13[12 + 25(8)] = 2,756

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Find the volume and surface area of the composite figure. Give your answer in terms of π.

irakobra [83]

Answer:

V = 240π cm^3 , S= 168π cm^2

Step-by-step explanation:

The given figure is a combination of hemi-sphere and a cone

Volume:

For volume

r = 6 cm

h = 8 cm

$Volume\ of\ cone = \frac{1}{3}\pi r^2h\\= \frac{1}{3}\pi (6)^2*8\\=\frac{1}{3}\pi *36*8\\=\frac{288}{3}\pi\\=96\pi cm^3 \\\\Volume\ of\ hemisphere = \frac{2}{3}\pi r^3\\=\frac{2}{3}*\pi * (6)^3\\=\frac{2}{3}*\pi *216\\=\frac{432}{3}\\=144\pi cm^3 \\\\Total\ Volume= Volume\ of\ cone + Volume\ of\ hemisphere\\= 96\pi +144\pi \\=240\pi cm^3$

Surface Area:

For this particular figure we have to consider the lateral area of the cone shape and surface area of the hemisphere

We have to find the lateral height

$l = \sqrt{r^2+h^2}\\ l = \sqrt{(6)^2+(8)^2} \\l= \sqrt{36+64}\\ l = \sqrt{100}\\l = 10cm\\\\Surface\ area\ of\ cone = \pi rl\\= \pi (6)(10)\\=\pi *60\\=60 \pi\ cm^2\\\\Surface\ area\ of\ hemisphere = 2\pi r^2\\= 2 \pi * (6)\\= 2 \pi *36\\= 72 \pi\ cm^2\\\\Total\ surface\ Area = Surface\ area\ of\ cone + Surface\ area\ of \ hemisphere\\= 60 \pi + 72 \pi\\=132 \pi\ cm^2$