Well, it's kind of inconvenient (bummer) not to know the formulas, because that's the whole point of this exercise ... knowing and using the formulas.
Here are the formulas you need. Cut this out and hang it on the fridge:
-- Volume of a cube = (side)³
-- Volume of a sphere = (4/3) (pi) (radius)³
-- Volume of a cylinder = (pi) (radius)² (height)
-- Volume of a cone = (1/3) (pi) (radius)² (height)
Use these formulas to find the volumes in #14, #15, and #16. Each picture is a combination of <u>two</u> of these shapes. #14 is a cube, plus half of a sphere on top of it. #15 is a short cylinder, plus a cone on top of it. #16 is a tall cylinder, minus half of a sphere carved out of the top end. ============================================ <em>#14).</em> This is a cube with sides=8cm PLUS half of a sphere whose radius is 4cm, sitting on top of the cube.
Volume of the cube = s³ = (8cm)³ = 512 cm³ Volume of the half-sphere = half of (4/3) (pi) (4)³ = 134.04 cm³
Volume of the combination = <em>646.04 cm³</em> ============================================= <em>#15).</em> This is a cylinder, with radius=16ft and height=4ft PLUS a cone, with radius=16ft and height=4ft, sitting on top of the cylinder.
Addum up ! ========================================= <em>#16).</em> This is a cylinder, with radius=6in and height=11in. MINUS half of a sphere, with radius=6in, scooped out of the top of the cylinder.
The area of a circular segment is given by .. A = (1/2)r^2*(θ -sin(θ)) . . . . . . . . . θ in radians .. = (1/2)*(27.8 in)^2*(5π/6 -sin(5π/6)) .. ≈ 818.4 in^2
