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
<h3>Which methods can be used to calculate the volume and surface area of the given figures?</h3>
Given:
The diameter of the cylinder = 12 cm
Height of the cylinder, <em>h</em> = 15 cm
Height of the cone, <em>h</em> = 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 =
Which gives;
Volume of the cylinder, V =
- V = π × (6 cm)² × 15 cm = 540·π cm³ ≈ <u>1,696.46 cm³</u>
ii) The surface area of a cone, = π·r·(r + √(h² + r²))
Surface area of the hemisphere = 3·π·r²
Which gives;
Surface area of ice cream cone, = π·r·(r + √(h² + r²)) + 3·π·r²
Where;
r = The radius of the cone = = 3 cm
<em> = </em>π ×3 × (3 + √(12² + 3²)) + 3·π·3² ≈ 229.68
- Surface area of ice cream cone, ≈<u> 229.68 cm²</u>
iii) The volume of 1 ice-cream, = × π × r² × 12 + × π × r³
Which gives;
= × π × 3² × 12 + × π × 3³≈ 169.45
- The volume of 1 ice-cream, = <u>169.45 cm³</u>
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 ≈<u> 565.49 cm²</u>
v) The number of ice-cream cones, <em>n</em>, that can be filled is given as follows;
The number of ice-cream cones that can be filled ≈ <u>10 cones</u>
Learn more about the volume of regular solids here:
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