MEDIUM
12th ICSE
IMPORTANT
Earn 100

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top by cutting off squares from the corners and folding up the flaps. What should be the side of the square in order that the volume of the box is maximum?

Important Questions on Applications of Derivatives

MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
Show that the semi-vertical angle of a cone of the maximum volume and of given slant height is cos-113.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
Show that the right circular cylinder of given volume, which is open at the top, has minimum total surface area if its height is equal to radius of its base.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
Show that a closed cylindrical vessel of given volume has the least (total) surface area when its height is twice its radius.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
A closed right circular cylinder has a volume of 2156 cu.cm. What will be the radius of its base so that its total surface area is minimum? Find the height of the cylinder when its total surface area is minimum.Take π=227.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
Show that the height of a closed right circular cylinder of given surface and maximum volume is equal to the diameter of base.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
Find the maximum volume of the cylinder which can be inscribed in a sphere of radius 33 cm.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
A cone is inscribed in a sphere of radius 12 cm. If the volume of the cone is maximum, find its height. 
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.8
A manufacturer plans to construct a cylindrical can to hold one cubic meter of oil. If the cost of constructing top and bottom of the can is twice the cost of constructing the side, what are the dimensions of the most economical can?