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Maths Case study (4 Marks)

Surface Areas and Volumes · Jharkhand Board (JAC) STD 9 (Jharkhand - English Medium). 10 questions.

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Case study (4 Marks)

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10 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
This is the picture of an ice-cream cone.
Image
The radius of the cone is $4\ cm$ and the height is $15\ cm$
An ice-cream seller keeps $1/4$ of it empty.
$10.$ What is the volume $($in $cm^3)$ of the empty part of the cone$?$
$A. 12π$
$B. 15π$
$C. 19π$
$D. 20π$
Answer
$D. 20π$
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Question 24 Marks
A company manufactures wooden boxes. Given below is the picture of an open wooden box.
Image
The height of the box is $25\ cm$
7. What is the surface area $($in $cm^2)$ of the box$?$
$A. 3500$
$B. 4700$
$C. 5900$
$D. 30000$
$8.$ A shopkeeper store cubes in it.
The side length of one cube is $9\ cm$
What would be the maximum number of cubes the shopkeeper can store in a box$? ($All cubes should be inside the box.$)$
$9.$ Rajan packs a football into a cubical cardboard box. The radius of the football is $11\ cm.$ Rajan keeps a margin of $1 \ cm$ from all the sides of the box while packing.
What is the side length of the cardboard box$?$
$A. 11\ cm$
$B. 20\ cm$
$C. 22\ cm$
$D. 24\ cm$
Answer
$7. B. 4700$
$8. 41 (30\times40\times25)/(9\times9\times9)= 41.15 .$ E $\times$ act answer $= 41$ as all cubes should it in it$)$
$9. D. 24 cm$
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Question 34 Marks
Raghav bought this planter.
Image
The radius of the rim is $14\ cm.$ The curved surface area of the planter is $1848\ cm^2$
$5.$ What is the height of the planter$?$
$6.$ What is the volume of the planter$?$
Answer
$5. 21 \ cm$
$6. 4116π\ cm^3$
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Question 44 Marks
This is the picture of a gas balloon illed with helium gas.
Image
This balloon has $18$ faces that are square in shape and $8$ equilateral faces that are triangular.
$3.$ Which of the following is the net of the balloon$?$
Image
$4.$ The side length of the square is $20\ cm.$ What is the total surface area of the balloon$?$
Answer
$3. A.$ Image
$4. (7200 + 800\sqrt3)$
$(7200 + 800\sqrt3) cm^2$
$8585.6 cm^2$
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Question 54 Marks
Raju designs a hut for homeless people. The hut is a combination of a cuboid and a right cone. The top of the hut is a cone with radius $4\ m$ and height $1\ m$. It is made of economical material. The loor of the tent is covered with rugs.
The total height of the tent is $4.5\ m.$ The cuboidal part of the tent is $6\ m$ long and $5\ m$ wide.
$1.$ What is the outer surface area $($in $m^2)$ of the hut$?$
$A. 77$
$B. 77+4π√17$
$C. 137+4π√17$
$D. 137+4π(4+√17)$
$2.$ The length and width of a rug used for the loor are $2.6\ m$ and $2\ m$ respectively.
What is the minimum number of rugs required to cover the loor of the tent house$?$
Answer
$1. B. 77+4π√17$
$2. 5$
$5$ rugs
$6$
$6$ rugs
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Question 64 Marks
Read the passage given below and answer any four questions: Sohan's house has one bedroom hall with kitchen. His son needed a separate room for study. Thus Sohan planned to construct a new room with length $4\ m,$ width $2\ m$ and the height $3\ m$ as shown in the following figure. The room was separate at the roof of the house. The dimensions of the bricks used are: $25cm \times 10\ cm \times 5\ cm$
.
$i.$ Total how many bricks will be required? $(1\ m^3 =1000000\ cm^3):$
$a. 30000$
$b. 40000$
$c. 28800$
$d. 27000$
$ii.$ How many bricks will be used on both walls along the length $($length $= 4\ m)$?
$a. 19200$
$b. 20200$
$c. 18800$
$d. 17000$
$iii.$ How many bricks will be used on both walls along the width $($width $= 3\ m)$?
$a. 19200$
$b. 9600$
$c. 10000$
$d. 15000$
$iv.$ What is the volume of the room?
$a. 24\ m^3$
$b. 1\ m^3$
$c. 20\ m^3$
$d. 15\ m^3$
What is the area of the floor?
$a. 10\ m^2$
$b. 12\ m^2$
$c. 8\ m^2$
$d. 8\ m^3$
Answer
$(i)$ $(c)$ $28800$
$(ii)$ $(a)$ $19200$
$(iii)$ $(b)$ $9600$
$(iv)$ $(a)$ $24\ m^3$
$(v)$ $(c)$ $8\ m^2$
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Question 74 Marks
Read the Source/ Text given below and answer these questions:

In Agra in a grinding mill, there were installed $5$ types of mills. These mills used steel balls of radius $5\ mm, 7\ mm,10\ mm, 14\ mm$ and $16\ mm$respectively. All the balls were in the spherical shape. For repairing purpose mills need $10$ balls of $7\ mm$ radius and $20$ balls of $3.5\ mm$ radius. The workshop was having $20000\ mm^3$ steel. This $20000\ mm^3$ steel was melted and $10$ balls of $7\ mm$ radius and $20$ balls of $3.5\ mm$ radius were made and the remaining steel was stored for future use. Answer the following questions:
$i.$ What was the volume of $10$ balls of radius $7\ mm?$
$a. 14373.3\ mm^3$
$b. 14000\ mm^3$
$c. 7000\ mm^3$
$d. 20000\ mm^3$
$ii.$ What was the volume of $20$ balls of radius $3.5\ mm$?
$a. 2000\ mm^3$
$b. 1800\ mm^3$
$c. 1796.6\ mm^3$
$d. 3593.3\ mm^3$
$iii.$ How much steel was kept for future use?
$a. 1250\ mm^3$
$b. 2033.3\ mm^3$
$c. 1300\ mm^3$
$d. 2200\ mm^3$
$iv.$ What was the surface area of one ball of $7\ mm$ radius?
$a. 600\ mm^2$
$b. 616\ mm^2$
$c. 308\ mm^2$
$d. 400\ mm^2$
$v.$ What was the surface area of one ball of $3.5\ mm$ radius?
$a. 600\ mm^2$
$b. 616\ mm^2$
$308\ mm^2$
$d. 154\ mm^2$
Answer
$(i)$ $(a)$ $14373.3\ mm^3$
$(ii)$ $(c)$ $1796.6\ mm^3$
$(iii)$ $(b)$ $2033.3\ mm^3$
$(iv)$ $(a)$ $600\ mm^2$
$(v)$ $(c)$ $308\ mm^2$
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Question 84 Marks
Read the Source Text given below and answer any four questions: Veena planned to make a jewellery box to gift her friend Reeta on her marriage. She made the jewellery box of wood in the shape of a cuboid. The jewellery box has the dimensions as shown in the figure below. The rate of painting the exterior of the box is $Rs. 2$ per $cm^2$. After making the box she took help from his friends to decorate the box. The blue colour was painted by Deepak, Black by Suresh, green by Harsh and the yellow was painted by Naresh.

$i.$ What is the volume of the box?
$a. 24000\ cm^3$
$b. 1200\ cm^3$
$c. 800\ cm^3$
$d. 600\ cm^3$
$ii.$ How much area did Suresh paint?
$a. 24000\ cm^2$
$b. 1200\ cm^2$
$c. 800\ cm^2$
$d. 600\ cm^2$
$iii.$How much area did Deepak paint?
$a. 24000\ cm^2$
$b. 600\ cm^2$
$c. 800\ cm^2$
$d. 1200\ cm^2$
$iv.$ What amount did Harsh charge?
$a. Rs. 800$
$b. Rs. 1200$
$c. Rs. 1600$
$d. Rs. 2000$
$v.$ What amount did Veena pay for painting:
$a. Rs. 2600$
$b. Rs. 5200$
$c. Rs. 5000$
$d. Rs. 6000$
Answer
$(i)$
$(a)$
$24000\ cm^3$
$(ii)$
$(b)$
$1200\ cm^2$
$(iii)$
$(d)$
$1200\ cm^2$
$(iv)$
$(c)$
$Rs. 1600$
$(v)$
$(b)$
$Rs. 5200$
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Question 94 Marks
Read the passage given below and answer these questions: Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying $300\ m^2$ cloth with them. As shown in the figure they made the tent with height $10\ m$ and diameter $14\ m$. The remaining cloth was used for the floor.
 
$i.$ How much Cloth was used for the floor?
$a. 31.6\ m^2$
$b. 166\ m^2$
$c. 106\ m^2$
$d. 206\ m^2$
$ii.$ What was the volume of the tent?
$a. 3006\ m^3$
$b. 1606\ m^3$
$c. 513.36\ m^3$
$d. 5006\ m^3$
$iii.$ What was the area of the floor?
$a. 506\ m^2$
$b. 1006\ m^2$
$c. 1506\ m^2$
$d. 1546\ m^2$
$iv.$ What was the total surface area of the tent?
$a. 4006\ m^2$
$b. 422.46\ m^2$
$c. 3006\ m^2$
$d. 4006\ m^2$
$v.$ What was the latent height of the tent?
$a.126\ m$
$b. 12.26\ m$
$c. 156\ m$
$d. 176\ m$
Answer
$(i)$ $(a)$ $31.66\ m^2$
$(ii)$ $(c)$ $513.36\ m^3$
$(iii)$ $(d)$ $1546\ m^2$
$(iv)$ $(b)$ $422.46\ m^2$
$(v)$ $(b)$ $12.26\ m$
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Question 104 Marks
Read the passage given below and answer these questions: Dev was doing an experiment to find the radius $r$ of a sphere. For this he took a cylindrical container with radius $R = 7\ cm$ and height $10\ cm$. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from $A$ to $B$ equal to $3.40\ cm.$

$i.$ What is the approximate radius of the sphere?
$a. 7\ cm$
$b. 5\ cm$
$c. 4\ cm$
$d. 3\ cm$
$ ii.$ What is the volume of the cylinder?
$a. 700\ cm^3$
$b. 500\ cm^3$
$c. 1540\ cm^3$
$d. 2000\ cm^3$
$iii.$ What is the volume of the sphere?
$a. 700\ cm^3$
$b. 600\ cm^3$
$c. 500\ cm^3$
$d. 523.8\ cm^3$
$ iv.$ How many litres water can be filled in the full container? $($Take $1$ litre $= 1000\ cm^3):$
$a. 1.50$
$b. 1.44$
$c. 1.54$
$d. 2$
$v.$ What is the surface area of the sphere?
$a. 314.3\ m^2$
$b. 300\ m^2$
$c. 400\ m^2$
$d. 350\ m^2$
Answer
$(i)$ $(b)$ $5\ cm$
$(ii)$ $(c)$ $1540\ cm^3$
$(iii)$ $(d)$ $523.8\ cm^3$
$(iv)$ $(c)$ $1.54$
$(v)$ $(a)$ $314.3\ m^2$
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