Apps. and Interpretation for IBDP Maths Ebook 1 | Page 189

Exercise 51
1. A plastic toy is in the shape of a sphere with radius 15 cm.
(a) Calculate the total surface area of the plastic toy.
The plastic toy is enlarged such that its total surface area is increased by 30%.
[2]
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(b)
Calculate the radius of the plastic toy following this increase.
[4]
2. A football in the shape of a sphere is filled with gas until the radius is 14 cm.
(a)
Calculate the total surface area of the football.
The total surface area of the football is increased by 15%.
[2]
(b)
Calculate the percentage increase of its volume.
[5]
3. The radius and the height of a cylindrical sponge cake are 18 cm and 8 cm respectively.
(a)
Calculate the total surface area of the sponge cake.
The sponge cake is then cut into two identical halves vertically by a knife.
[2]
(b)
Calculate the percentage increase of the total surface area.
[4]
4. The radius and the slant height of a crystal in the shape of circular cone are 7 cm and
25 cm respectively.
(a)
Calculate the total surface area of the crystal.
The crystal is then cut into two identical halves vertically.
[2]
(b)
Calculate the percentage increase of the total surface area.
[5]
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