The diagram shows a solid made up of a hemisphere and a cone. The base radius of the cone and the radius of the hemisphere are each 7 cm. The height of the cone is 13 cm. (a) (i) Calculate the total volume of the solid. [The volume of a hemisphere of radius r is given by V a 32 πr 3 .] [The volume of a cone of radius r and height h is given by V a 13 πr2h.] [2] (ii) The solid is made of wood and 1 cm3 of this wood has a mass of 0.94 g. Calculate the mass of the solid, in kilograms, correct to 1 decimal place. [3] (b) Calculate the curved surface area of the cone. [The curved surface area of a cone of radius r and sloping edge l is given by A a πrl .] [3] (c) The cost of covering all the solid with gold plate is $411.58. Calculate the cost of this gold plate per square centimetre. [The curved surface area of a hemisphere is given by A a 2πr 2 .] [5]
Answers
Answer:
Step-by-step explanation:
The formulas are as follows :
Volume of a hemisphere = 2/3πr^3
Volume of a cone = 1/3πr^2 h
The calculations :
a) Total volume of the solid.
Volume of the hemisphere is :
= 2/3 × 22/7 × 7^3 = 718.67 cubic centimeters.
Volume of the cone is :
= 1/3 × 22/7 × 7^2 × 13 = 667.33
Total volume = 718.67 + 667.33 = 1386 cubic centimeters.
= 1386 cubic centimeters.
b) mass of the solid.
If 1 cubic centimeters weigh 0.94 1386 cubic centimeters will weigh?
1386 × 0.94 = 1302.84 grams
In Kilograms we have :
1302.84/1000 = 1.30284 Kgs
= 1.3 kgs to one decimal place.
c) The curved surface area of the cone.
= 2 × 22/7 × 7 × 13 = 572 square centimeters.
d) The curved surface area of the hemisphere is :
= 2 × 22/7 × 7^2 = 308
Total surface area of the solid :
= 308 + 572 = 880 square centimeters
= 880 square centimeters.
The total amount required to paint this is 411.58
Per square centimeters it is :
411.58/880 = 0.4677
= $0.4677 per square centimeter.