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Tutors Answer Your Questions about Bodies-in-space (FREE)
Question 1189053: The core of a cast iron piece has the shape of a spherical segment of two bases. The radii of the upper and lower bases are 31 cm and 91 cm, respectively. The distance between the bases is 91 cm. find the weight of the core assuming that sand weighs 1600 kg per cubic meter.
Click here to see answer by math_tutor2020(3816)  |
Question 1189053: The core of a cast iron piece has the shape of a spherical segment of two bases. The radii of the upper and lower bases are 31 cm and 91 cm, respectively. The distance between the bases is 91 cm. find the weight of the core assuming that sand weighs 1600 kg per cubic meter.
Click here to see answer by ikleyn(52776)  |
Question 1190324: Three spherical planets of radius r are on orbits that keep them within viewing distances of one another. At any instant, each planet has a region that cannot be seen from anywhere on the other two planets. What is the total area of the three unseen regions?
Click here to see answer by ikleyn(52776) |
Question 1191467: the frustum has a regular hexagon on bases. the upper base measures 17 ft. on side and the lower base measures 27 ft. on a side. the altitude of the frustum is 15 ft. find the mass of the frustum, if its density is 97 lbs. per cu. ft.
Click here to see answer by greenestamps(13198)  |
Question 1192510: please tutor can you please help me figure out this problem. Thank you!
The 3rd planet from the sun, earth, is said to be 4.54 × 10^9 years old. Modern humans have been walking on this planet for 3.0 × 10^5 years**. What percentage of time has the modern human occupied the earth? Express your answer as a complete sentence using scientific notation.
Click here to see answer by Alan3354(69443)  |
Question 1193372: At what distance from the base of a right circular cone must a plane be passed parallel to the base in order that the volume of the frustum formed shall be three-fifths of the volume of the given cone?
Pls. if anyone can help me? I try the volume of the frustum formula but I still didn't get it but I know that the answer is 0.26319h. Hope anyone could notice me. Thank you very much. More power!
Click here to see answer by greenestamps(13198) |
Question 1193641: At what distance from the base of a right circular cone must a plane be passed parallel to the base in order that the volume of the frustum formed shall be three-fifths of the volume of the given cone.
Anyone could u pls. help me please how to get this one using a FORMULA of the cone or frustum. I kinda having a hard time figuring out how this problem will be solved using a formula. But I know one thing, its answer is 0.26319. thaaanks.
Click here to see answer by ikleyn(52776) |
Question 1194401: Find the total area of the frustum of a regular square pyramid which is inscribed
in the frustum of a cone whose upper and lower base diameters are 11 ft and 15 ft
respectively, and whose altitude is 19 ft.
Click here to see answer by ikleyn(52776) |
Question 1194400: A Dutch windmill in the shape of the frustum of a right circular cone is 17 meters
high. The diameters at the bottom and the top are 24 meters and 15 meters, the
inner diameters 18 meters and 9 meters. How many cubic meters of stone were
required to build it?
Click here to see answer by ikleyn(52776) |
Question 1195315: Imagine I wrap sheet metal part way around a tube leaving two parallel sides connected by a semicircle. Now imagine I remove the tube and cut the object so formed across both ends at an angle of 25 degrees to the axis of the semicircular surface to form a chute with vertical sides, vertical ends, and a semicicular chute surface at an angle of 25 degrees to the vertical.
In this case how can I precisely quantify the dimensions, and in particular specify a design plan for both the finished object and the cutting template for a piece of sheet metal that could be bent into the desired shape? In the template of the flattened opbject, what will be the angle between the four lines that will form the vertical ends of the completed chute (the ends of the two sides), and how can I specify the arc between them (semicircle in the final object, but arbitrary arc in the template)? I think the arc will still be circular, is that correct? (In which case it will be defined by the radius, the angle between the two lines, and the location of the centre of the arc).
Reason for the question: I need to make plans for a modified coffee grinder exit chute, from which someone can construct the part for me. The original chute is horizontal, the coffee grinds are pushed out in large clumps and then fall through a tube - not surprisingly the result is very poor. My aim is to make a new chute that falls at a steep slope right from the start, to prevent clumping.
Aside: Why not just us a bigger sheet, bend as described above and then cut at an angle, without working out the shape in flattened form? That would not be adequate because:
I have simplified the shape for the purposes of concentrating on the core problem, it is actually a little more complicated;
AND I have to rely on others to make the part, and need to provide an adequate job description for it;
AND I made various mock-ups in paper and foil ad lib for an earlier prototype at about 45 degrees (too flat), but found it is all the more difficult to do ad lib, the steeper is the slope. There are screw tabs at the top, which make it very difficult to draw accurately without being able to calculate the angles and arcs precisely.
Click here to see answer by ikleyn(52776) |
Question 1195315: Imagine I wrap sheet metal part way around a tube leaving two parallel sides connected by a semicircle. Now imagine I remove the tube and cut the object so formed across both ends at an angle of 25 degrees to the axis of the semicircular surface to form a chute with vertical sides, vertical ends, and a semicicular chute surface at an angle of 25 degrees to the vertical.
In this case how can I precisely quantify the dimensions, and in particular specify a design plan for both the finished object and the cutting template for a piece of sheet metal that could be bent into the desired shape? In the template of the flattened opbject, what will be the angle between the four lines that will form the vertical ends of the completed chute (the ends of the two sides), and how can I specify the arc between them (semicircle in the final object, but arbitrary arc in the template)? I think the arc will still be circular, is that correct? (In which case it will be defined by the radius, the angle between the two lines, and the location of the centre of the arc).
Reason for the question: I need to make plans for a modified coffee grinder exit chute, from which someone can construct the part for me. The original chute is horizontal, the coffee grinds are pushed out in large clumps and then fall through a tube - not surprisingly the result is very poor. My aim is to make a new chute that falls at a steep slope right from the start, to prevent clumping.
Aside: Why not just us a bigger sheet, bend as described above and then cut at an angle, without working out the shape in flattened form? That would not be adequate because:
I have simplified the shape for the purposes of concentrating on the core problem, it is actually a little more complicated;
AND I have to rely on others to make the part, and need to provide an adequate job description for it;
AND I made various mock-ups in paper and foil ad lib for an earlier prototype at about 45 degrees (too flat), but found it is all the more difficult to do ad lib, the steeper is the slope. There are screw tabs at the top, which make it very difficult to draw accurately without being able to calculate the angles and arcs precisely.
Click here to see answer by BM22222(1) |
Question 1195853: A circular cylinder having a length of 12 m has a radius of 3 m. If a wedge is cut from the cylinder by two planes, one perpendicular to the axis of the cylinder and the other passing through a diameter of the section made by the first plane and inclined to this plane at an angle of 45°. Find the volume of the wedge.
Click here to see answer by ikleyn(52776) |
Question 1195853: A circular cylinder having a length of 12 m has a radius of 3 m. If a wedge is cut from the cylinder by two planes, one perpendicular to the axis of the cylinder and the other passing through a diameter of the section made by the first plane and inclined to this plane at an angle of 45°. Find the volume of the wedge.
Click here to see answer by beezz(1) |
Question 1199755: Two identical spheres of diameter 6 cm have the same total volume as
a) one sphere with diameter 12 cm
b) four identical spheres each with diameter 3 cm
c) eight identical spheres each with diameter 4 cm
d) sixteen identical spheres each with diameter 3 cm
e) thirty-two identical spheres each with diameter 2 cm
Click here to see answer by greenestamps(13198) |
Question 1201413: A tall cylindrical container 6 cm in diameter contains some water. Nine steel spheres of diameter 4 cm are put into the water. If all the spheres are under water, and no water overflows from the container, then the rise in water level, in cm, is
a) 85 1/3 b) 21 1/3 c) 10 2/3 d) 9 e) 2 2/3
Click here to see answer by josgarithmetic(39616) |
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