Answer to Question #187581 in Geometry for John

Question #187581

a large cone has a height 6 cm and base diameter 18 cm. The large cone is made by placing a small cone of height 2 cm and base diameter 6 cm on top of a frustum B.


Calculate the volume of the frustum B. Give your answer in terms of π.​​​​​​​​

 

Calculate the total surface area of frustum B. Give your answer in terms of π.


1
Expert's answer
2021-05-07T12:31:22-0400

"Volume \\ of\\ frustum\\ of\\ cone=\\dfrac{{\\pi}h(r_1^{2}+r_2^{2}+r_1r_2)}{3}"

"r_1=9\\ cm"

"r_2=3\\ cm"

"\\ h=2\\ cm"

"where\\ r_1,r_2 \\ radius""\\ of\\ frustum\\ and\\ h_1\\ height\\ of frustum."

Now putting all the value in above formula, we get

"V=\\dfrac{{\\pi}h(r_1^{2}+r_2^{2}+r_1+r_2)}{3}=\\dfrac{{\\pi}\\times 2( 9^{2}+ 3^{2}+9\\times3)}{3}=78{\\pi}\\ cm^{3}"


"Total\\ surface \\ area \\ of frustum={\\pi}({r_1^{2}}+{r_2^{2}}+(r_1+r_2)\\times \\sqrt({{r_1-r_2})^{2}+h^{2}})=""{\\pi}\\times(9^{2}+3^{2}+9+3 +\\sqrt {(9-3)^{2}+2^{2}})"=216.64 "{\\pi}"


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