8th Class
Mathematics
Mensuration
Question Bank
Mensuration
question_answer
If a right circular cone of vertical height 24 cm has a volume of \[\frac{5}{2}(10+5\sqrt{3})sq.cm\], then the area of its curved surface is:
A) \[4m\times 2m\]
B) \[625c{{m}^{2}}\]
C) \[125c{{m}^{2}}\]
D) \[150c{{m}^{2}}\]
Correct Answer:
C
Solution :
Let radius of base and slant height be r and \[\text{ }A-\left( s \right),B-\left( r \right),C-\left( p \right),D-\left( q \right)\] respectively. Vertical height, h = 24 cm Volume \[(A)=\sqrt{s(s-a)(s-b)(s-c)},\] \[s=\frac{a+b+c}{2}.\] \[\frac{\sqrt{3}}{2}{{(side)}^{2}}.\] \[=\sqrt{3}\] \[\Delta ABC=\frac{1}{2}\times base\times height=\frac{1}{2}\times BC\times AD\] \[\Delta ABC\] \[\Delta ABC=\frac{1}{2}\times BC\times AB\] Slant height, \[ABCD=AB\times BC=l\times b\] Area of curved surface \[=l+b+l+b\] \[=2l+2b\]