Questions on Geometry: Bodies in space, right solid, cylinder, sphere answered by real tutors!

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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 ikleyn(52776)

Question 1201454: a cylindrical paint can is 5 inches across the top and about 12 inches high. How many cubic inches of paint could it hold (to the nearest hundredth)?
Click here to see answer by mananth(16946)

Question 1198553: The total surface area of a right circular cone is one and one-half times the lateral area. The radius of the base is equal to _______inches if the slant height is 6 inches.
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Question 1203546: Where does the line through (1, 2, 1) and (2, 1, 4) intersect the plane 2x + 3y + z = 10?
Click here to see answer by math_tutor2020(3816)

Question 1203638: A solid metal cylinder of height 6m and diameter 28cm is melted and recast into smaller solid cylinder. Each of the smaller cylinders is 14cm high and 0.5cm in diameter. How many smaller cylinders were obtained?
Click here to see answer by ikleyn(52776)

Question 1203825: A bullet of mass 180g is fired horizontally into a fixed wooden block with a speed of 24m/s. If the bullet is brought to rest in 0.4 seconds by a constant resistance, calculate the distance moved by the bullet in the wood.
Click here to see answer by ikleyn(52776)

Question 1196122: A particle moving in a straight line has initial velocity of 2 m/s at a point O on the line. The particle moves so that its acceleration is t seconds later is given by (2t-6) meter per second squared. Find the (a) Velocity when t= 5 seconds (b) Displacement of the particle in the fifth seconds.
Click here to see answer by Shin123(626)

Question 1207316: Could you let me know the number of planes of symmetry and the number of axes of rotation for the following?
(i) Cylinder
(ii) Cone
(iii) Square based pyramid
(iv) Rectangle based pyramid
(v) Equilateral triangle based pyramid
(vi) Isosceles triangle based pyramid
(vii) Scalene triangle based pyramid
Click here to see answer by ikleyn(52776)

Question 1198563: The bases of a frustum of a right circular cone are circles whose diameters are respectively 18 and 14 inches. With a slant height of 25 inches, the volume may be expressed as V = Χπ √γ in^3 where Χ and γ are integers. Find the smallest sum of Χ and γ.
Click here to see answer by CPhill(1959)

Question 1198562: The bases of a frustum of a right circular cone are circles whose diameters are respectively 18 and 14 inches. With a slant height of 25 inches, the volume may be expressed as V = Χπ √γ in^3 where Χ and γ are integers. Find the smallest sum of Χ and γ.
Click here to see answer by onyulee(41)

Question 1198559: The slant height of a right circular cone is 2 ft. At what distance from the vertex must the slant height be cut by a plane parallel to the base, in order that the lateral surface may be divided into two equal areas?
Click here to see answer by onyulee(41)

Question 1198557: The frustum of a cone of revolution is 25 cm high, and the radii of its bases are 8 cm and 2 cm, respectively. Find the height, in cm, of an equivalent right circular cylinder whose base is equal in area to the section of the frustum made by a plane parallel to its base and equidistant from the bases.
Click here to see answer by onyulee(41)

Question 1198556: A block of wood is in the form of a right circular cone. The altitude is 12 cm and the radius of the base is 5 cm. A cylindrical hole 5 cm in diameter is bored completely through the solid, the axis of the hole coinciding with the axis of the cone. The amount of wood left after the hole is bored may be expressed as V = Χπ/γ cm^3 where Χ is a positive integer and γ is a prime number. Find ∛χ + γ.
Click here to see answer by onyulee(41)

Question 1198555: A circular sector has a radius of 20 in. and a central angle of 120°. If this sector is cut out of paper and rolled so as to form the lateral surface of a right circular cone, find the total area and volume of the cone. The volume of the solid generated by this triangle may be expressed as V = βπ / σ √γ in^3 where β and σ are positive integers and γ is a prime number. Find the smallest sum of β,γ, and σ.
Click here to see answer by onyulee(41)

Question 1194335: The lateral edge of a pyramidal church spire is 92 ft. Each side of its octagonal base is 43 ft.What will be the cost of painting the spire at Php 530.00 a square foot?

Click here to see answer by proyaop(69)

Question 1185840: A baseball diamond is 90 ft in a side (it’s a square). Matthew runs from the first base to the second base at the rate of 3sqrt3 ft/sec. (a) How fast is his distance from the third base decreasing when he is 30 ft. from the first base? (b) At this instant, how fast is his distance from the home plate changing?
Click here to see answer by CPhill(1959)

Question 1181778: A factory's pressure tank rests on the upper base of a vertical pipe whose inside diameter is 1 and 1/2 ft. and whose length is 40 ft. The tank is a vertical cylinder surmounted by a cone, and it has a hemispherical base. If the alti tudes of the cylinder and the cone are respectively 6 ft. and 3 ft. and if all three parts of the tank have an inside diameter of 6 ft., find the volume of water in the tank and pipe when full.
Click here to see answer by CPhill(1959)

Question 1178404: in a laboratory, a chemist's measuring glass is conical in shape. if it is 8cm deep and 3 cm across the mouth, find the distance on the slant edge between the markings for 1 cc and 2 cc.
Click here to see answer by CPhill(1959)

Question 1172398: What is the volume of solid in xyz-space bounded by surfaces y = x^2, y = 2 - x^2, z = 0 and z = y + 3?
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Question 1172398: What is the volume of solid in xyz-space bounded by surfaces y = x^2, y = 2 - x^2, z = 0 and z = y + 3?
Click here to see answer by ikleyn(52776)

Question 1170318: The altitude of a right circular cylinder and the radius of its base are each 12 inches long. Two regular triangular prisms are inscribed in and circumscribed about the cylinder. Find the total surface areas of both prism
Click here to see answer by CPhill(1959)

Question 1210140: The base of right pyramid ABCDE is a rhombus with side 5. We also know that \triangle ABD \cong \triangle CBD and EA=BA=2. Find the volume of the pyramid.

Click here to see answer by CPhill(1959)

Question 1210141: The area of a cross section of a sphere is 64\% of the largest possible cross sectional area of the sphere. If the sphere has radius 1/2, what is the area of the cross section?

Click here to see answer by CPhill(1959)

Question 1210153: A and B are two points on a sphere of radius 2. We know the space distance between A and B is 2, What is distance from A to B along the (minor) arc of a great circle?

Click here to see answer by Edwin McCravy(20054)

Question 1210244: The area of a cross section of a sphere is 64\% of the largest possible cross sectional area of the sphere. If the sphere has radius 1/2, what is the area of the cross section?
Click here to see answer by greenestamps(13198)

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