Surface Area and Volume of Combination of Solids Questions
Here we are going to see, some practice questions on based on finding surface area and volume of combination of solids.
Question 1 :
A capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. If the length of the entire capsule is 12 mm and the diameter of the capsule is 3 mm, how much medicine it can hold?
Capacity of capsule
= 2 Volume of hemisphere + volume of cylinder
= 2(2/3) πr3 + πr2h
= (4/3) πr3 + πr2h
Height of Capsule
= 2 (radius of hemisphere) + height of cylinder
2(3/2) + h = 12
3 + h = 12
h = 12 - 3 = 9
= πr2 [(4/3) r + h]
= (22/7) (3/2)2[(4/3)(3/2) + 9]
= (22/7) (9/4)[2 + 9]
= (11/7) (9/2)(11)
= 77.78 cm3
Question 2 :
As shown in figure a cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid.
Surface area of solid
= surface area of cube + curved surface area of hemisphere - area of base of hemisphere
= 6a2 + 2πr2 - πr2
= 6a2 + πr2
= 6(7)2 + (22/7) (7/2)2
= 294 + 38.5
= 332.5 cm2
Question 3 :
A right circular cylinder just enclose a sphere of radius r units. Calculate (i) the surface area of the sphere (ii) the curved surface area of the cylinder (iii) the ratio of the areas obtained in (i) and (ii).
radius of sphere = height of cylinder/2
(i) the surface area of the sphere = 4πr2
(ii) the curved surface area of the cylinder
= 2π r h
= 2π r(2r)
(iii) the ratio of the areas obtained in (i) and (ii).
= 4πr2 : 4πr2
= 1 : 1
Question 4 :
A shuttle cock used for playing badminton has the shape of a frustum of a cone is mounted on a hemisphere. The diameters of the frustum are 5 cm and 2 cm. The height of the entire shuttle cock is 7 cm. Find its external surface area.
Surface area of shuttle cock = curved surface area of frustum cone + curved surface area of hemisphere
= π (R + r) l + 2πr2 ----(1)
Height of shuttle cock = 7
radius of hemisphere + height of frustum cone = 7
1 + h = 7
h = 6
l = √(h2 + (R - r)2)
l = √(62 + ((5/2) - 1)2)
l = √(36 + (9/4)
l = √153/2
l = 12.36/2
l = 6.18
By applying the value of l in (1), we get
= π ((5/2) + 1) l + 2πr2
= π[(7/2)(6.18) + 2 (1)2]
= (22/7)[(21.63 + 2]
= 74.26 cm2
After having gone through the stuff given above, we hope that the students would have understood, how to solve problems on surface area and volume of combination of solids.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Converting customary units worksheet
Customary units worksheet
Integers and absolute value worksheets
Nature of the roots of a quadratic equation worksheets
Trigonometry heights and distances
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Converting repeating decimals in to fractions