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Surface Area and Volume Maths - Surface Area and Volume

Maharashtra Board - STD 9 - Maths (MSBSHSE - English Medium). 50 questions in this chapter.

Question types

Surface Area and Volume question types

50 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

50
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5
Question groups
5
Question types
Sample Questions

Surface Area and Volume questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 11 Mark Question1 Mark
Make a cone and a hemisphere of cardsheet such that radii of cone and hemisphere are equal and height of cone is equal to radius of the hemisphere.
Fill the cone with fine sand. Pour the sand in the hemisphere. How many cones are required to fill the hemisphere completely ?

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Q 21 Mark Question1 Mark
Finding total surface area of sphere.
i. Take a sweet lime (Mosambe), Cut it into two equal parts.Image
ii. Take one of the parts. Place its circular face on a paper. Draw its circular border. Copy three more such circles. Again, cut each half of the sweet lime into two equal parts.
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iii. Now you get 4 quarters of sweet lime. Separate the peel of a quarter part. Cut it into pieces as small as possible. Try to cover one o’f the circles drawn, by the small pieces. Observe that the circle gets nearly covered.
The activity suggests that,
Curved surface area of a sphere = $4\pi r^2$
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Q 31 Mark Question1 Mark
Prepare a cylinder of a card sheet, keeping one of its faces open. Prepare an open cone of card sheet which will have the same base-radius and the same height as that of the cylinder. Pour fine sand in the cone till it just fills up the cone. Empty the cone in the cylinder. Repeat the procedure till the cylinder is just filled up with sand. Note how many coneful of sand is required to fill up the cylinder.

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Q 41 Mark Question1 Mark
Curved surface area of cone.

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Circumference of base of the cone = 2πr
As shown in the figure (c), make pieces of the net as small as possible. Join them as shown in the figure (d),. By joining the small pieces of net of the cone, we get a rectangle ABCD approximately.
Total length of AB and CD is 2πr.
∴ length of side AB of rectangle ABCD is πr and length of side CD is also πr.
Length of side BC of rectangle = slant height of cone = l.
Curved surface area of cone is equal to the area of the rectangle.

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Q 62 Mark Question2 Marks
The inner diameter of a well is 4.20 metre and its depth is 10 metre. Find the inner surface area of the well. Find the cost of plastering it from inside at the rate ₹ 52 per sq.m.
Given: Inner diameter (d) = 4.2 m,
To find: depth (h) = 10 m,
rate of plastering = ₹ 52 per sq.m.
Inner surface area and total cost of plastering
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Q 72 Mark Question2 Marks
Total surface area of a cone is 616 sq.cm. If the slant ‘height of the cone Is three times the radius of its base, find its slant height.
Given: Total surface area of a cone = 616 sq.cm., slant height of the cone is three times the radius of its base
To find: Slant height (l)
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Q 92 Mark Question2 Marks
Find the radius of a sphere if its volume is 904.32 cubic cm. (π = 3.14)
Given: Volume of sphere = 904.32 cubic cm.
To find: Radius of a sphere
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Q 113 Mark Question3 Marks
The length of a road roller is 2.1 m and its diameter is 1.4 m. For levelling a ground 500 rotations of the road roller were required. How much area of ground was levelled by the road roller? Find the cost of levelling at the rate of ₹ 7 per sq.m.
Given: For road roller,
diameter (d) = 1.4 m,
length (h) = 2.1 m
number of rotations required for levelling the ground = 500,
rate of levelling = ₹ 7 per sq. m.
To find: Area of ground leveled by the road roller and cost of levelling
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Q 123 Mark Question3 Marks
If diameter of a road roller is $0.9\ m$ and its length is $1.4\ m,$ how much area of a field will be pressed in its $500$ rotations?$\left(\pi=\frac{22}{7}\right)$
Given: For road roller,
diameter $(d) = 0.9\ m,$ length $(h) = 1.4\ m$
To find: Area of a field pressed in $500$ rotations
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Q 133 Mark Question3 Marks
Volume of a hemisphere is $18000  \pi$ cubic cm . Find its diameter.
Given: Volume of hemisphere $=18000  \pi$ cubic cm .
To find: Diameter of the hemisphere
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Q 143 Mark Question3 Marks
Find the surface area of a sphere, if its volume is $38808$ cubic $cm .\left(\pi=\frac{22}{7}\right)$
Given: Volume of sphere $= 38808$ cubic cm.
To find: Surface area of sphere
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Q 153 Mark Question3 Marks
If the surface area of a sphere is $2826 cm^2$ then find its volume. $(\pi = 3.14)$
Given: Surface area of sphere = $2826 sq.cm.$
To find: Volume of sphere
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Q 164 Mark Question4 Marks
If the ratio of radius of base and height of a cone is 5 : 12 and its volume is 314 cubic metre. Find its perpendicular height and slant height (π = 3.14).
Given: Ratio of radius of base and height of a cone = 5 : 12,
Volume = 314 cubic metre
To find: Perpendicular height (h) and slant height (l)
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Q 175 Mark Question5 Marks
To make an open fish tank, a glass sheet of 2 mm gauge is used. The outer length, breadth and height of the tank are 60.4 cm, 40.4 cm and 40.2 cm respectively. How much maximum volume of water will be contained in it ?
Given: Thickness of the glass = 2 mm,
outer length of the tank = 60.4 cm,
outer breadth of the tank = 40.4 cm,
outer height of the tank = 40.2 cm
To find: Volume of water fish tank contains
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Q 185 Mark Question5 Marks
In a field, dry fodder for the cattle is heaped in a conical shape. The height of the cone is 2.1 m and diameter of base is 7.2 m. Find the volume of the heap of the fodder. If it is to be covered by polythene in rainy se&son then how much minimum polythene
sheet is needed?$\left(\pi=\frac{22}{7}\right.$ and $\left.\sqrt{17.37}=4.17\right]$
Given: Height of the heap (h) = 2.1 m.
diameter of the base (d) = 7.2 m
$\therefore$ Radius of the base $(r)=\frac{d}{2}=\frac{7.2}{2}=3.6 m$
To find: Volume of the heap of the fodder and polythene sheet required
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Q 195 Mark Question5 Marks
Find the volume of a cone, if its total surface area is $7128 sq . cm$ and radius of base is 28
$cm .\left(\pi=\frac{22}{7}\right)$
Given: Radius $(r)=28 cm$,
Total surface area of cone $=7128$ sq.cm
To find: Volume of the cone
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