Question

A glass with a bottom and a top inside radius of 5 cm and 7.5 cm respectively, and a height of 5 inches, was filled with water until the brim. A solid spherical ball was dropped inside resulting in the water overflowing and spilling, creating a wet area on the table. The ball has a radius of 4 cm. Find: (a) the volume of the water spilled (assuming the glass remained full to the brim) and (b) the area of the wet area assuming that the spilled water was evenly distributed on the table at 1 mm thickness.

Name: a glass with a bottom and a top inside radius of 5cm and 75cm respectively and a height of 5inches was filled with water until the brim a solid spherical ball was dropped inside resulting fo 67738
Uploaded: 2022-05-12T12:39:48-08:00
Duration: 3 min 27 s
Channel: Andrew Terry
Description: a glass with a bottom and a top inside radius of 5cm and 75cm respectively and a height of 5inches was filled with water until the brim a solid spherical ball was dropped inside resulting fo 67738

          A glass with a bottom and a top inside radius of 5 cm and 7.5 cm respectively, and a height of 5 inches, was filled with water until the brim. A solid spherical ball was dropped inside resulting in the water overflowing and spilling, creating a wet area on the table. The ball has a radius of 4 cm. Find: (a) the volume of the water spilled (assuming the glass remained full to the brim) and (b) the area of the wet area assuming that the spilled water was evenly distributed on the table at 1 mm thickness.

Added by Alfonso S.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Andrew Terry

05/12/2022

Step 1

Given the top radius, \( r_1 = 7.5 \, \text{cm} \), bottom radius, \( r_2 = 5 \, \text{cm} \), and height, \( h = 12.7 \, \text{cm} \) (converted from 5 inches). Using the formula for the volume of a frustum: \[ V_{\text{frustum}} = \frac{1}{3} \pi h (r_1^2 + Show more…

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A glass with a bottom and a top inside radius of 5 cm and 7.5 cm respectively, and a height of 5 inches, was filled with water until the brim. A solid spherical ball was dropped inside resulting in the water overflowing and spilling, creating a wet area on the table. The ball has a radius of 4 cm. Find: (a) the volume of the water spilled (assuming the glass remained full to the brim) and (b) the area of the wet area assuming that the spilled water was evenly distributed on the table at 1 mm thickness.