The surface area of a cylinder is given by the formula 2πrh + 2πr². However, since the cylinder is open at both ends, we don't include the area of the bases in our calculation. So, we only need to calculate the area of the curved surface, which is given by 2πrh.

First, let's calculate the surface area:
A = 2πrh
A = 2π * 3.0 cm * 15.0 cm
A = 282.6 cm²

Now, let's calculate the absolute uncertainty. The formula for the absolute uncertainty in a product or quotient is given by:

ΔA/A = Δr/r + Δh/h

Substituting the given values:

ΔA/282.6 = 0.1/3.0 + 0.1/15.0
ΔA = 282.6 * (0.0333 + 0.00667)
ΔA = 282.6 * 0.04
ΔA = 11.3 cm²

So, the surface area of the cylinder is (282.6 ± 11.3) cm². The closest answer to this is (280 ± 10) cm², so the answer is A.

Question

The surface area of a cylinder is given by the formula 2πrh + 2πr². However, since the cylinder is open at both ends, we don't include the area of the bases in our calculation. So, we only need to calculate the area of the curved surface, which is given by 2πrh.

First, let's calculate the surface area:
A = 2πrh
A = 2π * 3.0 cm * 15.0 cm
A = 282.6 cm²

Now, let's calculate the absolute uncertainty. The formula for the absolute uncertainty in a product or quotient is given by:

ΔA/A = Δr/r + Δh/h

Substituting the given values:

ΔA/282.6 = 0.1/3.0 + 0.1/15.0
ΔA = 282.6 * (0.0333 + 0.00667)
ΔA = 282.6 * 0.04
ΔA = 11.3 cm²

So, the surface area of the cylinder is (282.6 ± 11.3) cm². The closest answer to this is (280 ± 10) cm², so the answer is A.

Knowee AI · Accepted Answer

The surface area of a cylinder is given by the formula 2πrh + 2πr². However, since the cylinder is open at both ends, we don't include the area of the bases in our calculation. So, we only need to calculate the area of the curved surface, which is given by 2πrh.

First, let's calculate the surface area:
A = 2πrh
A = 2π * 3.0 cm * 15.0 cm
A = 282.6 cm²

Now, let's calculate the absolute uncertainty. The formula for the absolute uncertainty in a product or quotient is given by:

ΔA/A = Δr/r + Δh/h

Substituting the given values:

ΔA/282.6 = 0.1/3.0 + 0.1/15.0
ΔA = 282.6 * (0.0333 + 0.00667)
ΔA = 282.6 * 0.04
ΔA = 11.3 cm²

So, the surface area of the cylinder is (282.6 ± 11.3) cm². The closest answer to this is (280 ± 10) cm², so the answer is A.

A hollow cylinder, which is open at both ends, has a radius of (3.0 ± 0.1) cm and a length of(15.0 ± 0.1) cm.What is the value, with its absolute uncertainty, of the surface area of the cylinder?A (280 ± 10) cm2B (282.7 ± 0.2) cm2C (420 ± 30) cm2D (424.1 ± 0.3) cm2

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