Mathematics, 12.04.2021 22:10 david2154

A cylinder has a radius of 4 inches and a height of 5 inches. If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders? Answer in terms of Pi.

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Answer from: narutoxptheninja

Question:-

A cylinder has a radius of 4 inches and a height of 5 inches. If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders ? Answer in terms of Pi.

Answer:-Given:-

A cylinder has a radius of 4 inches and a height of 5 inches.

To Find:-

If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders ?

Solution:-Let in case of 1st cylinder,

$\bullet$ Radius (r_1) is 4 inches

$\bullet$ Height is 5 inches

And in case of 2nd cylinder,

$\bullet$ Radius (r_2) is 3 × 4 = 12 inches [as in the question it is given that the radius of the cylinder is tripled]

$\bullet$ Height is 5 inches

Now,

Surface area (s_1) of 1st cylinder

is 2πr(r + h) = 2π × 4(4 + 5)

= 8π(9)

= 72π sq inches

Surface area (s_2) of 2nd cylinder

is 2πr(r + h) = 2π × 12(12 + 5)

= 24π(17)

= 408π sq inches

$\therefore$ The difference in the surface areas of the two cylinders is = $(s_2 \: - \: s_1)$ = (408π - 72π) = 336π sq inches

The difference in the surface areas of the two cylinders is 336π sq inches. [Answer]

Answer from: Quest

Abit confused about what you mean, but i think you might be referring to slope intercept form: y = mx + bin that case b, or the y intercept is already given.(0,-1)find the slope by using the formulay2 - y1/x2 - x1the final slope will be 4/2, equivalent to 2.now your equation should look like thisy = 4/2x -1sorry if this didn’t you out!

Answer from: Quest

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

a₁ = $ 30 000

r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

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