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imagine a large spherical-shaped vegetable 16 cm in diameter. it can easily come

ID: 2878474 • Letter: I

Question

imagine a large spherical-shaped vegetable 16 cm in diameter. it can easily come apart in layers that are 1cm thick. a worm bores a cylindrical hole of radius r through the center of the solid vegetable of radius R(r<R). Find the volume of the solid that remains by using:).> A. Cylindrical shells
B. Disks/washers imagine a large spherical-shaped vegetable 16 cm in diameter. it can easily come apart in layers that are 1cm thick. a worm bores a cylindrical hole of radius r through the center of the solid vegetable of radius R(r<R). Find the volume of the solid that remains by using:).> A. Cylindrical shells
B. Disks/washers imagine a large spherical-shaped vegetable 16 cm in diameter. it can easily come apart in layers that are 1cm thick. a worm bores a cylindrical hole of radius r through the center of the solid vegetable of radius R(r<R). Find the volume of the solid that remains by using:).> A. Cylindrical shells
B. Disks/washers imagine a large spherical-shaped vegetable 16 cm in diameter. it can easily come apart in layers that are 1cm thick. a worm bores a cylindrical hole of radius r through the center of the solid vegetable of radius R(r<R). Find the volume of the solid that remains by using:).> A. Cylindrical shells
B. Disks/washers

Explanation / Answer

Let the diameter of the sphereical vegetable be=16cm

layers of the sphere =1cm thick

radius of the hole bore by worm=r

radius of solid vegetable =R

=diamter of the sphere/2 = 16/2 =8cm

1)Find the volume of solid that remains by using cylindrical shells

A)4/3*pi*r^3 = volume of the sphere

pi*r^2*h=volume of cylinder

volume of cylindrical shells = 4*pi*8^3 - pi * r^2*h

= 2143.57- pi*r^2*1

where h=1cm =height of layer

=2143.57 -3.14*r

B)find the volume of the solid that remains using disks/washers

=pi*R^2*h -pi*r^2*h

=pi*R^2-pi*r^2

where h=1cm

=pi(R^2-r^2)