Prisms

The solid prism has constant cross section which is a trianle sides 8cm, 7cm and 7cm long respectively. If the lenght of the prism is 9cm, calculate the volume of the prism.

  1. 👍 0
  2. 👎 0
  3. 👁 73
  1. Recall that the area of a prism is just area of the base times height. In this case, the base is the triangle. Since the lengths of side of triangle are given, we use Heron's formula to get first the area:
    A = √(s(s-a)(s-b)(s-c))
    where
    a, b & c = lengths of side of triangle
    s = half of the perimeter = 1/2*(a+b+c)
    Substituting,
    s = 1/2*(7+7+8)
    s = 1/2*(22)
    s = 11
    A = √(s(s-a)(s-b)(s-c))
    A = √(11(11-7)(11-7)(11-8))
    A = √(11(4)(4)(3))
    A = √(528)
    A = 4√(33) = 22.98 cm^2

    Finally, we multiply this to the height of the cylinder to get the volume:
    V = A*h
    V = 22.98*9
    V = 206.8 cm^3

    Hope this helps~ :)

    1. 👍 0
    2. 👎 0
    posted by Jai

Respond to this Question

First Name

Your Response

Similar Questions

  1. geometry

    Fin the volume of a triangular prism with height 16cm, base (a right triangle with sides 7cm, 8cm, and 10cm and the right angle between shorter sides.)

    asked by Jastine on September 19, 2012
  2. math

    what is the volume of a rectangular prism 5.0cm long, 3.8cm wide and 2.7cm high?

    asked by brianna on September 6, 2012
  3. Please Check My Math Answers. Thanks!

    Can someone please be kind enough to check my answers? Thanks! :) I put stars by my answers. 1. Calculate the slant height for the given cone. Round to the nearest tenth. Diameter= 8cm Height= 9cm a. 10.2 cm b. 11.4 cm c. 9.8 cm

    asked by OceanBreeze on March 10, 2015
  4. Trigonometry

    a diagram shows a cross section of a triangular prism. AB=BC=7cm. BM=5cm m is the midpoint of the line segment AC. a) explain why angle AMB must be a right angle. b) calculate angle BCM. c) calculate area of the triangle

    asked by zoya on September 22, 2012
  5. Geometry

    Can a triangle have sides with the given lengths? Explain. 15) 8cm, 7cm, 9cm 16) 7ft, 13ft, 6ft 17) 20in, 18in, 16in 18) 3m, 11m, 7m

    asked by Hannah on November 29, 2010
  6. math

    The base of a triangular prism is a right triangle whose legs are 7cm and 24 cm. The height of the prism is 30cm. What is lateral area of prism?

    asked by lacy on September 24, 2014
  7. Geometry

    I have a model of a triangle shaped pyramid with sides 6cm base 8cm and height 7cm. If I enlarge the pyramid using a scale factor of 1.2, what will the new perimeter and area be?

    asked by Tami on April 11, 2016
  8. math

    A 4cm x 5cm x 7cm rectangular prism is painted on all faces. If the prism is cut into 1cm x 1cm x 1cm cubes, how many cubes do not have paint on any of its sides?

    asked by k on March 17, 2016
  9. Math

    A rectangle prism has a length of 8 cm with 3 cm and height 5 cm what are the dimensions of the horizontal cross section ? A. 8 cm by 5cm B.8cm by 3cm C. 5cm by 3cm D. 8 cm by 8cm

    asked by Aa on January 31, 2018
  10. Math ASAP

    1. What is the length of the diagonal for the rectangular prism with L=8cm W=3cm H=7cm to the nearest whole unit? 10 cm 11 cm

    asked by Anonymous on March 18, 2016

More Similar Questions