Betelgeuse is a red supergiant star in the constellation Orion. It radiates heat

Question

Betelgeuse is a red supergiant star in the constellation Orion. It radiates heat at the rate of 2.70 × 1030 W and has a surface temperature of 3000 K. Assuming that it is a perfect emitter, what is the radius of Betelgeuse? The Stefan-Boltzmann constant is 5.670 × 10-8 W/m2 · K4.

Question 31 options:

8.70 × 1010 m

7.80 × 1010 m

1.90 × 1011 m

2.16 × 1011 m

1.40 × 1011 m

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3.

Question 33 options:

131 cm

79 cm

6.6 cm

37 cm

8.70 × 1010 m

7.80 × 1010 m

1.90 × 1011 m

2.16 × 1011 m

1.40 × 1011 m

Explanation / Answer

2.16 × 1011 m

6.6cm

density steel 7750 to 8050 kg/m ³, use 7870
density of water at 20C = 0.998 g/cm ³ = 998 kg/m ³


The overall density must be equal to that of water, 998 kg/m ³
volume = V = â´/₃πr ³ = â´/₃π(1.5) ³ = 14.14 m ³
Mass = 998 kg/m ³ x 14.14 m ³ = 14109 kg

Density of steel = 7870 kg/m ³ = 14109 kg / V
V = 1.79 m ³

So the volume of steel is 1.79 m ³ out of a total volume of 14.14 m ³

Volume of shell is â´/₃πr1 ³ – â´/₃πr2 ³ = â´/₃π(r1 ³ – r2 ³) = 1.79
r1 ³ – r2 ³ = 0.428 m ³
r2 ³ = (1.5) ³ - 0.428
r2 = 1.434

Thickness is 1.5 – 1.434 = 0.066 m or 6.6 cm

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