please ans following ques 1 The curved surface area of a cone is 60 pie cm - Maths - Surface Areas and Volumes

Question

please ans following ques
1 The curved surface area of a cone is 60 pie cm
square slant height is 8cm find the radius of base

2 how many metres of cloth 5m wide will be required to make a
conical tank the radius of whose base is 7cm , and whose height is
24 m
3 The ratio of 2 cylinders are in the ratio 2:3 , and their
heights are in the ratio 5:3 find the ratio of their volume

Aakash Sharma · Accepted Answer

(1) Let the radius of base of the given cone be r cm Given: Slant height (l) = 8 cm and curved surface Area = 60Ï€ cm2 $\Rightarrow π r l = 60 π \Rightarrow r = \frac{60}{r} = \frac{60}{8} = 7 5$ Hence radius of base is 7 5 m (2) Given: Radius of base (r) and height (h) of the conical tank are 7 m and 24 m $\Rightarrow Slant height (l) = \sqrt{r^{2} + h^{2}} = \sqrt{{(7 m)}^{2} + (24 m)^{2}} = \sqrt{49 m^{2} + 576 m^{2}} = \sqrt{625 m^{2}} = 25 m$ Thus $curved surface area = π r l = \frac{22}{7} \times 7 \times 25 m^{2} = 550 m^{2}$ Now let x m of cloth is required Then C S A of conical tank = area of cloth $\Rightarrow 5 x = 550 \Rightarrow x = \frac{550}{5} = 110$ Hence 110 m of cloth is required to make the required conical tank (3) Let the radii of base of the cylinders be 2x and 3x and height be 5y and 3y Then $Required ratio = \frac{π (2 x)^{2} 5 y}{π (3 x)^{2} 3 y} = \frac{4 x^{2} \times 5 y}{9 x^{2} \times 3 y} = \frac{20}{27} = 20 : 27$