Find the volume of a right pyramid that has a square base in the xy-plane. – 1 < a <1, -1 < y < 1, and thevertex at (0, 0, 3). The graph shows a pyramid with the vertex at (0,0,3). Your problem will have a differentvalue for the vertex. Round your answer to four decimal places.Pyramid2--1-0.505Os 0 Osy

Given right pyramid with square base. Side length(a)= 2 units Height(h)= 3 units

Answered: Find the volume of a right pyramid that…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 31E

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Similar questions

the region bounded by the graph y = 3x - x3, the y axis, and the line y = 2 is revolved about y axis. The solid of revolution is ______ . A. Disk B. WasherC. Cylindrical Shell D. Pyramid
Consider the graph of y2 = x(4 − x)2 , as shown in the figure. Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the x-axis, (b) the y-axis, and (c) the line x = 4.
Fit a least-squares parabola having the form y = a + bx + cx2 to the given data. x 1.2 1.8 3.1 4.9 5.7 7.1 8.6 9.8 y 4.5 5.9 7 7.8 7.2 6.8 4.5 2.7 What is the value of a? What is the value of b?What is the value of c?What is the estimate the of y at x=1.2
The parabola y=(1/2)x² divides the disk x² + y² ≤ 8 into two parts (see figure). Find the area of each part. To solve this problem, perform the following i. Find the points of intersection. ii. Let A₁ be the region bounded by √(8 - x²) above by the parabola below. (a Trig substitution will be needed) iii. Let A₂ be the region bounded by the parabola above and by the disk below. (area of the disk- area of A₁)
The base of a garden tent is a square with side length c feet. Two semi-circular poles run between pairs of opposite vertices of the base and support the tent. Cross-sections parallel to the base are squares. Compute the volume enclosed by the tent as follows: (a) Establish a rectangular coordinate system with its origin at the center of the tent’s base, the positive y-axis pointing directly upward through the tent’s apex, and the postive x-axis passing through a vertex of the base. Sketch the tent with this coordinate system. Label the axes with their variable names and units. (b) Sketch the cross-section of the tent cut out by the xy-plane (a semi-circle) in the xy-coordinate system. Label the coordinates of the intercepts of the semi-circle. Label the axes with their variable names and units. (c) Sketch a general horizontal segment with its endpoints P and Q on the semicircle in part (b). Label the coordinates of its endpoints P and Q as (−x, y) and (x, y), respectively. Assume x…
the base of a solid is the region in the first quadrant bounded by the y-axis, the x-acis, the graph of y=e^x, and the verticle line x=1. For the solid, each cross section perpendicular to the x-axis is a square . what is the volumne of the solid? a. e-1 b.1/2e^2-1/2 c.e^2-1 d.2e^2-2
1. The graph above shows the base of an object. Compute the exact value of the volume of the object, given that cross-sections (perpendicular to the base) are equiangular triangles. 2. Find the volume formed by rotating about the y-axis the region enclosed by:x=3yx=3y and y3=xy3=x with y≥0y≥0 3. A volume is described as follows:1. the base is the region bounded by y=3−349x2y=3-349x2 and y=0y=02. every cross-section parallel to the x-axis is a triangle whose height and base are equal.Find the volume of this object.volume = ______________
1 a)Given that the volume of the solid under the paraboloid z = x^2+y^2and above the disk x^2+y^2 ≤ 169 is mπ/2.find the value of m. b) Find the surface area of the part of the surface z=x^2+3ythat lies above the triangular region T in the xy-plane with the vertices (0, 0), (1, 0), and (1, 6).Give your answer in 2 decimal places.You have to use the following formula: A(S)=∬T√(1+(∂z/∂x)^2+(∂z/∂y)^2) dA
The solid limited by the surfaces, (see solid and surfaces in the attached images):If V is the volume of the previous solid, then it is true that:
(b). A regulated-size rugby ball can be modelled as a solid of revolutionformed by revolving the graph ofy = -0.0944 x^2+3.4. - 5.5 ≤x≤5.5about x-axis. Compute the volume of the regulated size rugby ball(x and y are measured in inches) by using this model.
1. You must use section 6.3 of Stewart's book Stewart 7 edition to solve the following exercise. Determine the volume of the solid obtained by rotating the positive part of the parabola y=-x2+4x-3 around the x-axis.
1. Determine the value of a so that A= 2i +aj +k and B= 4i-2j-2k are perpendiculara. 1 unit b. 2 units c. 3 units d. 4 units2. Evaluate (i-2k)•( j +3k)a. 0 b. 1 c. 6 d. -63. What is the volume of a parallelepiped whose edges are represented by A= 2i-3j+4k,B= i+2j-k, and C= 3i-j+2ka. 7 cubic units b. 8 cubic units c. 9 cubic units d.10cubic units4.A vector which is not a null is calleda. resultant vector c. proper vectorb. rectangular vector d. component vectors5. Which of the following properties will be used when two or more vectors areperpendicular?a. dot product c.triple productb. cross product d. either a or b

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