S.chand publication New Learning Composite mathematics solution of class 7 Chapter 14 Perimeter and Area Exercise 14E

 Exercise 14E

Question 1

Find the circumference of each circle. Give your answer in terms of π

(a) diameter=9 cm

Circumference =πd

=9π cm

(b) diameter=87mm

Circumference =πd

=87π mm

(c) radius=18 cm

Circumference=2πr

=2×π×18

=36π cm

(d) radius$=39\frac{1}{2}$ m

$=\frac{79}{2}$ m

Circumference=2πr

$=2\pi \frac{79}{2}$

=79π m

Question 2

Use $\pi =\frac{22}{7}$ to find the circumference of each circle

(a) diameter=21 cm

Circumference=πd

$=\left(\frac{22}{7} \times 21\right)$ cm

=66 cm

(c) radius=42 cm

Circumference$=\left(2\times \frac{22}{7} \times 42\right)$ cm

=264

(d) radius=35.7 cm

Circumference$=\left(2 \times \frac{22}{7} \times 35.7 \right)$ cm

=224.4 cm

Question 3

Use π=3.14 to find the circumference of each circle

(a) diameter=20 mm

Circumference=(3.14×20) mm

=62.80 mm

(b) diameter=15 cm

Circumference=(3.14×15) cm

=47.10 cm

(c) radius=5 m

Circumference=(2×3.14×2) km

=12.56 km

Question 4

Find the length of a diameter of a circle whose circumference is 44 cm (take $\pi=\frac{22}{7}$ )

Let, the diameter be d

ATQ,

$\frac{22}{7}d=44$

$d=\frac{44\times 7}{22}$

∴d=14

Ans : The length of the diameter is 14 cm

Question 5

Find the radius of a circle whose circumference is 314 cm (take π=3.14)

Let ,the radius of a circle be r

ATQ

2×3.14×r=314

$r=\frac{3.14}{2\times 3.14}$

r=50

Ans : Radius of the circle is 50 cm

Question 6

The diameter of Ravi's bicycle tyre measure 63 cm. How far does the bicycle move when the wheel makes one complete revolution (Take $\pi =\frac{22}{7}$)

We know that,

Distance covered by bicycle in 1 revolution=Circumference of the cycle's wheel

∴Circumference of the cycle's wheel$=\frac{22}{7} \times 63$ cm

=198 cm

Question 7

Let , the radius be r

ATQ,

2×3.14×r=125.6

$r=\frac{125.6}{2\times 3.14}$

r=20

Ans : The length of the radius of the garden is 20 m

Question 8

Let , the diameter of the pool be d

ATQ,

$\frac{23}{7} \times d=176$

$d=\frac{7}{22} \times 176$

∴d=56

Ans : She swam 56 cm

Question 9

Approximate circumference of the earth at the equator $=\left(\frac{22}{7} \times 12754\right)$ km

=40084 km

Question 10

(a)

Figure to be added

Circumference of ABC$=\left(\frac{1}{2} \times 3.14 \times 8\right)$ cm

=12.56 cm

Circumference of CDE$=\left(\frac{1}{2} \times 3.14 \times 8\right)$ cm

=12.56

Circumference of EFG$=\left(\frac{1}{2} \times 3.14 \times 8\right)$ cm

=12.56

Circumference of GHA$=\left(\frac{1}{2} \times 3.14 \times 8 \right)$

=12.56

Perimeter of the shape=4×12.56 cm

=50.24 cm

(b)

Figure to be added

Perimeter of the ABC$=\left(\frac{1}{4} \times 2\times 3.14 \times 16\right)$ mm

=25.12 mm

Perimeter of the whole shape ABCD

=(25.12+16+16)mm

=57.12

(c)

Figure to be added

Radius of the semi-circle$=\frac{40}{2}$ m

=20 m

∴Circumference of the semi-circle$=\left(\frac{1}{2}\times 2\times 3.14 \times 20\right)$ m

=62.8 m

Question 11

Figure to be added

Let, the radius of the smaller circle be r

∴Circumference of smaller circle=2πr

Circumference of smaller circle=2π(r+5)

∴Difference of circumference=2π(r+5)-2πr

=2π(r+5-r)

=2×3.14 5

=31.4 m

=10π 

Question 12

Figure to be added

The sum of the diameter of the four circle is equal to the diameter of the largest circle

∴Sum of the circumference of four small circle

=circumference of the largest circle

Question 13

Circumference of the circle=(2×π×16) cm

=32π cm

Perimeter of the re-arrangement shape=(32π+16+16) cm

=(32π+32) cm

Ans : Yes, perimeter is increased by 32 cm

Question 14

Circumference of the wheel $=\left(2 \times \frac{22}{7} \times 70\right)$ cm

=440

The wheel makes 10 revolution in 5 sec

∴Distance covered=(440×10) cm

=4400 cm

=44 m

∴Speed of the wheel$=\frac{44}{5}$ m/s

=8.8 m/s