answer:For the cube with side length 3, each side has an area of 3^2 = 9, and with 6 sides, the total surface area is 6 times 9 = 54. For the sphere, if r is the radius and it has the same surface area as the cube, we have: [ 4pi r^2 = 54 ] [ r^2 = frac{54}{4pi} = frac{27}{2pi} ] [ r = sqrt{frac{27}{2pi}} = frac{3sqrt{6}}{sqrt{2pi}} = frac{3sqrt{3}}{sqrt{pi}} ] The volume V of the sphere is: [ V = frac{4}{3} pi r^3 = frac{4}{3} pi left(frac{3sqrt{3}}{sqrt{pi}}right)^3 ] [ V = frac{4}{3} pi cdot frac{27 sqrt{27}}{pi sqrt{pi}} = frac{4}{3} cdot 27 sqrt{frac{27}{pi}} ] [ V = 36 sqrt{frac{27}{pi}} = 36 cdot frac{3sqrt{3}}{sqrt{pi}} = frac{108sqrt{3}}{sqrt{pi}} ] Setting this equal to frac{L sqrt{15}}{sqrt{pi}} gives: [ 108 sqrt{3} = L sqrt{15} ] [ L = frac{108 sqrt{3}}{sqrt{15}} = frac{108 sqrt{3}}{sqrt{3} sqrt{5}} = frac{108}{sqrt{5}} = frac{108 sqrt{5}}{5} = frac{108 times 2.236}{5} approx 48.384 ] Therefore, boxed{L approx 48}.

answer:1. **Identify the given information and the problem statement**: We are given that the sum of two angles of a triangle is frac{4}{3} of a right angle, and one of these two angles is 40^circ larger than the other. 2. **Convert the fraction of the right angle to degrees**: Since a right angle is 90^circ, frac{4}{3} of a right angle is: [ frac{4}{3} times 90^circ = 120^circ ] Therefore, the sum of the two angles is 120^circ. 3. **Set up an equation for the two angles**: Let x be the measure of the smaller angle. Then, the measure of the larger angle, which is 40^circ more than the smaller angle, is x + 40^circ. The equation representing their sum is: [ x + (x + 40^circ) = 120^circ ] Simplifying this equation: [ 2x + 40^circ = 120^circ implies 2x = 120^circ - 40^circ = 80^circ implies x = frac{80^circ}{2} = 40^circ ] Thus, the smaller angle is 40^circ. 4. **Calculate the measure of the second angle**: Since the second angle is 40^circ larger than the first: [ x + 40^circ = 40^circ + 40^circ = 80^circ ] Hence, the second angle is 80^circ. 5. **Use the Triangle Sum Theorem to find the third angle**: The Triangle Sum Theorem states that the sum of the angles in a triangle is 180^circ. Thus, the third angle is: [ 180^circ - (40^circ + 80^circ) = 180^circ - 120^circ = 60^circ ] So, the third angle is 60^circ. 6. **Determine the largest angle**: Comparing the angles 40^circ, 80^circ, and 60^circ, the largest angle is 80^circ. 7. **Conclusion**: The degree measure of the largest angle in the triangle is 80^circ. The final answer is boxed{textbf{(C)} 80}

answer:If Shannon has 48.0 heart-shaped stones and wants to use 8.0 stones in each bracelet, we can calculate the number of bracelets she can make by dividing the total number of stones by the number of stones per bracelet. Number of bracelets = Total number of stones / Number of stones per bracelet Number of bracelets = 48.0 / 8.0 Number of bracelets = 6.0 Shannon can make boxed{6} bracelets with heart-shaped stones.

answer:Let's denote the speeds of A, B, and C as Va, Vb, and Vc respectively. Given that A can give B a 70-meter start in a kilometer race, it means that when A covers 1000 meters, B covers 930 meters (1000 - 70). Similarly, when A can give C a 200-meter start, it means that when A covers 1000 meters, C covers 800 meters (1000 - 200). Now, let's find the ratio of their speeds. Since speed is distance over time, and they all run for the same amount of time in this scenario, we can use their distances covered as a direct comparison of their speeds. The ratio of A's speed to B's speed is: Va : Vb = 1000 : 930 The ratio of A's speed to C's speed is: Va : Vc = 1000 : 800 Now, we want to find out how much start B can give C in a kilometer race. To do this, we need to find the ratio of B's speed to C's speed. Since Va : Vb = 1000 : 930 and Va : Vc = 1000 : 800, we can write: Vb / Va = 930 / 1000 Vc / Va = 800 / 1000 To find the ratio of Vb to Vc, we can divide the two equations: (Vb / Va) / (Vc / Va) = (930 / 1000) / (800 / 1000) Simplifying this, we get: Vb / Vc = (930 / 1000) * (1000 / 800) Vb / Vc = 930 / 800 Vb / Vc = 1.1625 This means that for every 1.1625 meters B runs, C runs 1 meter. To find out how much start B can give C in a 1000-meter race, we can set up the following equation: 1.1625 * (1000 - x) = 1000 Where x is the start that B can give C. Solving for x: 1.1625 * 1000 - 1.1625x = 1000 1162.5 - 1.1625x = 1000 1.1625x = 1162.5 - 1000 1.1625x = 162.5 x = 162.5 / 1.1625 x ≈ 139.78 Therefore, B can give C approximately boxed{139.78} meters start in a kilometer race.