To find the area of the hemispherical surface (a), we first need to calculate the radius of the hemispherical part.
We know that the diameter of the hemispherical part is 70 cm, so the radius can be calculated by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 70 cm / 2 = 35 cm
The formula to calculate the surface area of a hemisphere is:
Surface Area of Hemisphere (A) = 2Ï€r^2
Plugging in the value of the radius we just calculated, we get:
A = 2Ï€(35 cm)^2
= 2Ï€(1225 cm^2)
= 2450Ï€ cm^2
So the area of the hemispherical surface is 2450Ï€ cm^2.
To find the total surface area of the model (b), we need to calculate the lateral surface area of the frustum of the cone and add it to the area of the hemispherical surface.
The formula for the lateral surface area of a frustum of a cone is:
Lateral Surface Area of Frustum of a Cone (A_f) = π(R_1 + R_2)l
Where R_1 and R_2 are the radii of the top and bottom circles of the frustum, and l is the slant height.
We know that the radius of the top circle (R_1) is equal to the radius of the hemispherical part (35 cm), and the radius of the bottom circle (R_2) is half the base diameter of the frustum (28 cm / 2 = 14 cm). The slant height (l) is given as 60 cm.
Plugging in these values into the formula, we get:
A_f = π(35 cm + 14 cm)(60 cm)
Calculating this, we get:
A_f = 49Ï€(60 cm)
= 2940Ï€ cm^2
Now, to find the total surface area (A_total), we need to add the area of the hemispherical surface (2450Ï€ cm^2) and the lateral surface area of the frustum (2940Ï€ cm^2):
A_total = A + A_f
= 2450Ï€ cm^2 + 2940Ï€ cm^2
= (2450 + 2940)Ï€ cm^2
= 5390Ï€ cm^2
So, the total surface area of the model is 5390Ï€ cm^2.