Respuesta :
The volume and surface area of the ice cream cone are given by adding
the volume and surface area of the component parts.
Responses (approximate values)
i) 1,696.46 cm³
ii) 229.68 cm²
iii) 169.45 cm³
iv) 565.49 cm²
v) 10 cones
Which methods can be used to calculate the volume and surface area of the given figures?
Given:
The diameter of the cylinder = 12 cm
Height of the cylinder, h = 15 cm
Height of the cone, h = 12 cm
Diameter of the cone, D = 6 cm
Shape of the cap of the cone = Hemispherical
i) The capacity of the container = The volume of the cylinder
Volume of a cylinder = Area of base × height
Radius of the cylinder, R = [tex]\mathbf{\dfrac{D}{2}}[/tex]
Which gives;
[tex]R = \dfrac{12 \, cm}{2} = 6 \, cm[/tex]
Volume of the cylinder, V = [tex]\pi \times R^2 \times h[/tex]
- V = π × (6 cm)² × 15 cm = 540·π cm³ ≈ 1,696.46 cm³
ii) The surface area of a cone, [tex]A_c[/tex] = π·r·(r + √(h² + r²))
Surface area of the hemisphere = 3·π·r²
Which gives;
Surface area of ice cream cone,[tex]A_{ch}[/tex] = π·r·(r + √(h² + r²)) + 3·π·r²
Where;
r = The radius of the cone = [tex]\dfrac{6 \, cm}{2}[/tex] = 3 cm
[tex]A_{ch}[/tex] = π ×3 × (3 + √(12² + 3²)) + 3·π·3² ≈ 229.68
- Surface area of ice cream cone,[tex]A_{ch}[/tex] ≈ 229.68 cm²
iii) The volume of 1 ice-cream, [tex]V_{ic}[/tex] = [tex]\frac{1}{3}[/tex] × π × r² × 12 + [tex]\frac{2}{3}[/tex] × π × r³
Which gives;
[tex]V_{ic}[/tex] = [tex]\frac{1}{3}[/tex] × π × 3² × 12 + [tex]\frac{2}{3}[/tex] × π × 3³≈ 169.45
- The volume of 1 ice-cream, [tex]V_{ic}[/tex] = 169.45 cm³
iv) The CSA of the cylindrical container is given as follows;
Curves Surface Area of a cylinder, CSA = 2·π·R·h
- CSA = 2 × π × 6 cm × 15 cm ≈ 565.49 cm²
v) The number of ice-cream cones, n, that can be filled is given as follows;
[tex]n = \dfrac{V}{V_{ic}}[/tex]
[tex]n = \dfrac{1,696.46 \, cm^3}{169.45 \, cm^3/cone} \approx 10 \ cones[/tex]
The number of ice-cream cones that can be filled ≈ 10 cones
Learn more about the volume of regular solids here:
https://brainly.com/question/13338580
