Answer:
Q1)
GIVEN :-
- Diameter = 9m ⇒ Radius (r) = 9/2 = 4.5m
- Slant height (l) = 13m
TO FIND :-
- Surface area of the whole figure.
FORMULAES TO KNOW BEFORE SOLVING :-
- Curved surface area of cone = [tex]\pi rl[/tex] (where r = radius & l = slant height)
- Curved surface area of hemisphere = [tex]2\pi r^2[/tex] (where r = radius)
PROCEDURE :-
In the figure , the cone is mounted on a hemisphere.
⇒ Radius of cone = Radius of hemisphere = 4.5m
Total surface area of the figure = Curved surface area of both cone & hemisphere.
⇒
- Curved surface area of cone = [tex]\pi rl = 3.14 \times 4.5 \times 13 = 183.69m^2[/tex] ≈ 183.7m²
- Curved surface area of hemisphere = [tex]2\pi r^2 = 2 \times 3.14 \times (4.5)^2 = 127.17m^2[/tex] ≈ 127.1m²
∴ Total surface area = 183.7 + 127.1 = 310.8m²
Q2)
GIVEN :-
TO FIND :-
- Volume of hemisphere
- Surface area of hemisphere
FORMULAES TO KNOW BEFORE SOLVING :-
- Volume of hemisphere = [tex]\frac{2}{3} \pi r^3[/tex] (where r = radius)
- Surface area of hemisphere = [tex]2\pi r^2[/tex] (where r = radius)
PROCEDURE :-
Volume of hemisphere = [tex]\frac{2}{3} \pi r^3 = \frac{2}{3} \times 3.14 \times (3)^3 = 56.52km^3[/tex] ≈ 56.5km³
Surface area of hemisphere = [tex]2\pi r^2 = 2 \times 3.14 \times (3)^2 = 56.52km^2[/tex] ≈ 56.5km²
