the right triangle has sides of 15 cm and 20 cm.
the hypotenuse of this right triangle is equal to sqrt(15^2 + 20^2) = 25.
label your triangle ABC where B is the right angle and AB has a length of 20 and BC has a length of 15.
the hypotenuse of this triangle has a length of 25 which is AC.
draw a line from B to intersect line AC at D so that BD is perpendicular to AC at D.
you can use trigonometry or you can use geometry to find the length of BD.
i'll use geometry since this appears to be a geometry question.
if you look at the diagram of your right triangle, you will see that angle A is common to triangle ABC and ABD.
diagram is at the bottom of this presentation.
this means that angle ABD of triangle ABD and angle ACB of triangle ABC are equal.
this means that triangle ABD is similar to triangle ABC.
since they are similar, their corresponding sides are proportional.
this means that BD is to AB as BC is to AC.
this forms the ratio of BD/AB = BC/AD.
we replace labels with lengths that we know to get:
BD/20 = 15/25
we solve for BD to get:
BD = (15*20)/25 = 12.
we now know the following about our right triangle.
AB = 20
BC = 15
BD = 12
AC = 25
we can now solve for AD and DC by using pythagorus formula on triangles ABD and BCD.
this gets us:
AD = 16
CD = 9the complete measurements are in section 1 of the attached diagram.
if you revolve this right triangle around it's hypotenuse, you will get a cross section figure as shown in section 2 of the attached diagram.
the 3 dimensional picture of this is in section 3 as best i can render it.
you have 2 cones.
they are cones ABB' and CBB'
the volume of each cone is given by the formula of 1/3 * pi * r^2 * h
r is the radius of the base of each cone which is equal to 12.
h is the heiight of each cone which is 16 for cone 1 and 9 for cone 2.
ABB' is cone 1
CBB' is cone 2
volume of cone 1 is 1/3 * pi * 12^2 * 16 which becomes 1/3 * pi * 144 * 16 which simplifies to 768 * pi.
volume of cone 2 is 1/3 * pi * 12^2 * 9 which becomes 1/3 * pi * 144 * 9 which simplifies to 432 * pi.
total volume of the double cone is 768 * pi + 432 * pi = 1200 * pi.
if you use 3.14 for pi, then the total volume would be 1200 * 3.14 = 3768.
that's the volume.
the surface area would be the lateral surface area of each cone which is given by the formula of pi * r * l where:
r is the radius of the base.
l is the lateral height of each of the cones.
the lateral height of cone 1 is 20
the lateral height of cone 2 is 15.
the lateral surface area of cone 1 is pi * 12 * 20 = 240 * pi.
the lateral surface area of cone 2 is pi * 12 * 15 = 180 * pi.
the total surface area of the resulting double cone figures is 240 * pi + 180 * pi which equals 420 * pi.
using 3.14 for pi, this comes out to be equal to 420 * 3.14 = 1318.8
since you are dealing in cm, then your answer would be:
volume = 3768 cubic cm.
surface area = 1318.8 square cm.
