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Maths Case study (4 Marks)

Surface Areas and Volumes · Jharkhand Board (JAC) STD 10 (Jharkhand - English Medium). 5 questions.

Questions

Case study (4 Marks)

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

Question 14 Marks

To make the learning process more interesting, creative and innovative, Amayras' class teacher brings clay in the classroom, to teach the topic-Surface Areas and Volumes. With clay, she forms a cylinder of radius 6cm and height 8cm. Then she moulds the cylinder into a sphere and asks some questions to students.
  1. During the conversion of a solid from one shape to another the volume of new shape will be Increase, Decrease or Remain unaltered?
  2. The radius of the sphere so fanned is:
  3. The volume of the sphere so formed is:
    Or
    Find the ratio of the volume of sphere to the volume of cylinder.
Answer
1.Remain unaltered2. 6cm
$3.905.14cm^3$​​​​​​​
Or
1:1
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Question 24 Marks
One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is 24cm and base radius is 7cm. While watching this, some questions came into Rinku's mind. Help Rinku to find the answer of the following questions.
  1. After carving out cone from the cylinder,
  2. Find the slant height of the conical cavity so formed.
  3. The curved surface area of the conical cavity so formed is:
    Or
    External curved surface area of the cylinder is:
Answer
1.Volume of the cylindrical wood will decrease.2. 25cm
$3.550cm^2$
Or
$1056cm^2$​​​​​​​
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Question 34 Marks
Meera and Dhara have 12 and 8 coins respectively each of radius 3.5cm and thickness 0.5cm. They place their coins one above the other to form solid cylinders.

Based on the above information, answer the following questions.
  1. When two coins are shifted from Meera's cylinder to Dharas cylinder, then,
  2. The ratio of curved surface area of the cylinders made by Meera and Dhara is:
  3. Curved surface area of the cylinder made by Meera is:
    Or
    The volume of the cylinder made by Dhara is:
Answer
1. Volume of two cylinder become equal.2. 3:2
$3.132cm^2$
Or
$154cm^3$​​​​​​​
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Question 44 Marks
To promote cooperation, culture, creativity, sharing, self-confidence, and other social values, a student adventure camp was organized by the school for X-class students and their accommodation was planned in texts. The teacher divides the students into groups, each group of four students was given to prepare a conical tent of radius 7m and canvas of area $551m^2$​​​​​​​ in which $1m^2 $is used in stitching and wasting of canvas:
  1. Find Curved surface of conical tent.
  2. Find Height of the conical tent.
  3. Find Volume of tent.
    Or
    How much space is occupied by each student in the tent?
Answer
1. $\pi\text{rl}$2. 24m
$3. 1232m^3$
Or
$308m^3$
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Question 54 Marks

Due to heavy floods in a state, thousands of people were homeless. 50 schools collectively offered to the state government to provide the place and the canvas for 1500 tent to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8m and height 3.5m, with the conical upper part of the same base radius but of height 2.1m. $(\text{use}\ \pi=\frac{22}7)$
  1. Area of canvas used to make the tent is:
  2. The volume of the tent is:
  3. If the canvas used to make the tent cost ₹120 per sq.m, find the amount to be paid by the schools for making the tents.
    Or
    Amount shared by each school to set-up the tents.
Answer
1. CSA of cylindrical portion + CSA of the conical portion2. $\pi\text{r}^2(\frac13\text{r}+\text{h})$ cubic units
3. ₹ 11088
Or
₹ 332640
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