Question

Isosceles triangle, whose base is 14 ft and legs 25 ft long, is given. Triangle is rotated around the line that contains one of the legs of the triangle. Determine the surface area and the volume of the obtained solid without using calculus.​

Answer 1

Given:

length of isosceles triangle, $l=25\ ft$

Base of triangle, $b=14\ ft$

To Find: surface area and the volume obtained

Step-by-step explanation:

• When it is rotated around the line which contain one leg of the triangle, it becomes the cone as shown in figure.

• Surface area of the cone

$A=\pi r(r+h^{2} +r^{2} )$

$=\dfrac{22}{7}\times7(7+(24)^{2}+7^{2})\\=13904\ ft^{2}$

$h=\sqrt{25^{2}-7^{2} }\\=576\\h=24\ ft$

$V=\dfrac{1}{3} \pi r^{2}h\\=\dfrac{1}{3}\times\dfrac{22}{7}\times(7)^{2}\times24$

$=1232\ ft^{3}$

• The surface area is $13904$ and the Volume of cone is $1232\ ft^{3}.$