Question 1166787
i believe the book is correct.


here's why.


the surface area of a sphere is equal to 4 * pi * r^2


the surface area of a hemisphere would be half of that.


therefore, the surface area of the larger hemisphere is equal to 4 * pi * 11^2 / 2 = 760.2654222, .....


and the surface area of the smaller hemisphere is equal to 4 * pi * 6^2 / 2 = 226.1946711.


the sum of their areas is equal to 986.4600932 square centimeters.


but, that's not the total surface area that's exposed.


the base of each hemispheres is a circle whose area is equal to pi * r^2.


the area of the bases that is exposed is the area of the base of the larger hemisphere minus the area of the base of the smaller hemisphere.


that exposed area is equal to pi * 11^2 minus pi * 6^2 = 267.0353756 square centimeters.


add that to 986.4600932 to get a total exposed area of 1253.495469 square centimeters.


you can round as required.


here's my diagram of the situation as i see it.


<img src = "http://theo.x10hosting.com/2020/100801.jpg" >