Question

Help with these geometry problems, please! 10th grade geometry

Answer 1

Step-by-step explanation:

3.

the left cup is the summary of 2 cylinders.

the right cup is just a cone.

the volume of a cone is

pi×r²×h/3 = pi×3.5²×6/3 = pi×12.25×2 = pi×24.5 =

= 76.93 in³

the volume of a cylinder is

pi×r²×h

the first cylinder is

pi×3²×1.5 = pi×9×1.5 = pi×13.5 = 3.14×13.5 = 42.39 in³

the second cylinder is

pi×2²×2.25 = pi×4×2.25 = pi×9 = 28.26 in³

in total the cup has

42.39 + 28.26 = 70.65 in³

so, the cone has the larger volume by 6.28 in³ ≈ 6 in³.

that would be 3.479827 fl.oz. ≈ 3 fl.oz. of water.

I have no idea on what scale you need to quantify the amount of water. I just guessed.

2.

here we need the surface area.

the object consists of a large prism (or block) and a cylinder.

we don't need the bottom area for neither, as the cylinder is simply on top of the prism, and its bottom is not going to be painted either.

we need 5 sides of the prism :

front and back

left and right

top (and we need the full top, because the area the cylinder is covering up is the same area for the top of the cylinder).

and the we need to add only the side wall of the cylinder the "mantle".

so,

front and back rectangles are 10×3 × 2 = 60 in²

left and right rectangles are 10×3 × 2 = 60 in²

the top rectangle (square) is 10×10 = 100 in²

the cylinder mantle is

circumference of the circle × height

2×pi×r×h = 2×pi×4×6 = 3.14×48 = 150.72 in²

so, in total we have

60 + 60 + 100 + 150.72 = 370.72 in² ≈ 371 in²