Answer:
36 cm
43.27 cm
Step-by-step explanation:
[tex]r_1[/tex] = Radius of bucket = 18 cm
[tex]h_1[/tex] = Height of bucket = 32 cm
[tex]r_2[/tex] = Radius of cone
[tex]h_2[/tex] = Height of cone = 24 cm
The volume of the cylindrical bucket and the conical heap of sand is equal so
[tex]\pi r_1^2h_1=\dfrac{1}{3}\pi r_2^2h_2\\\Rightarrow r_2=\sqrt{\dfrac{3r_1^2h_1}{h_2}}\\\Rightarrow r_2=\sqrt{\dfrac{3\times 18^2\times 32}{24}}\\\Rightarrow r_2=36\ \text{cm}[/tex]
The radius of the heap is 36 cm.
Slant height is given by
[tex]l=\sqrt{r_2^2+h_2^2}\\\Rightarrow l=\sqrt{36^2+24^2}\\\Rightarrow l=43.27\ \text{cm}[/tex]
The slant height of the heap is 43.27 cm.
