Answer:
Height = 4 cm and slant height = 5 cm
Step-by-step explanation:
Given that,
The surface area of the cone, A = 75.4 cm²
Radius, r = 3 cm
The surface area of the cone is given by the formula as follows :
[tex]A=\pi r^2+\pi rl[/tex]
Put all the values,
[tex]75.4=3.14\times 3^2+3.14\times 3\times l\\\\75.4=28.26+9.42l\\\\75.4-28.26=9.42l\\\\47.14=9.42l\\\\l=\dfrac{47.14}{9.42}\\\\l=5\ cm[/tex]
Also,
[tex]l^2=r^2+h^2\\\\h=\sqrt{l^2-r^2}\\\\h=\sqrt{5^2-3^2}\\\\h=4\ cm[/tex]
Hence, the height of the cone is 4 cm and the slant height is 5 cm.
