Ice Cream Cone Calculations
1) To find the height of a triangle we need to use
The Pythagorean Theorem, a² + b² = c² ⇒ / 3² + b² = 6²
9 + b² = 36
-9 -9 =
√b² = √27 = 3√3 ≅ 5.2in
^
3 9
^
3 3
2) Area of triangle: (BASE)(HEIGHT)2/ 6 x 5.2 ÷ 2 = 15.6 x 2 = 31.2in²
↳We multiply by two to get
the Area of the top and
bottom triangle.
3) Area of Rectangle: (Base) x (Height) / 6 x 1 = 6 x 2 = 12in²
↳We multiply by two to get
the Area of the two rectangles.
4) Volume: (Area of Base)(Altitude) / 15.6 x 1 = 15.6in³
5) Volume of Cylinder: πr²h / π3² x 1 = 9π 9π2
↳We divide by two because we are
figuring out the volume of Half a
cylinder.
6) Surface Area of Cylinder: 2πrh + 2πr / 2π 3 x 1 + 2π 3 =
6π + 18π = 24π2 = 12π
↳We divide by two
because we are finding the
Surface Area of Half a
cylinder.
7) Volume = 9π2+ 15.6in³
8) S.A = Area of all sides added
31.2 + 12+ 12π = 43.2 + 12π in²
The Pythagorean Theorem, a² + b² = c² ⇒ / 3² + b² = 6²
9 + b² = 36
-9 -9 =
√b² = √27 = 3√3 ≅ 5.2in
^
3 9
^
3 3
2) Area of triangle: (BASE)(HEIGHT)2/ 6 x 5.2 ÷ 2 = 15.6 x 2 = 31.2in²
↳We multiply by two to get
the Area of the top and
bottom triangle.
3) Area of Rectangle: (Base) x (Height) / 6 x 1 = 6 x 2 = 12in²
↳We multiply by two to get
the Area of the two rectangles.
4) Volume: (Area of Base)(Altitude) / 15.6 x 1 = 15.6in³
5) Volume of Cylinder: πr²h / π3² x 1 = 9π 9π2
↳We divide by two because we are
figuring out the volume of Half a
cylinder.
6) Surface Area of Cylinder: 2πrh + 2πr / 2π 3 x 1 + 2π 3 =
6π + 18π = 24π2 = 12π
↳We divide by two
because we are finding the
Surface Area of Half a
cylinder.
7) Volume = 9π2+ 15.6in³
8) S.A = Area of all sides added
31.2 + 12+ 12π = 43.2 + 12π in²