61. The length of the diagonal and the breadth of a rectangle are 17 cm and 8 cm
respectively. Find its perimeter (in cm).
1) 92
2) 46
3) 42
4) 84
62. The area of a semicircle is 1925 cm2. Calculate its perimeter (in cm).
1) 360
2) 80
3) 160
4) 180
63. The surface area of a sphere is 5544 cm Find its diameter (in cm).
1) 42
2) 21
3) 84
4) 63
Answers
Question 1.
The length of the diagonal and the breadth of a rectangle are 17 cm and 8cm respectively. Find its perimeter.
Answer:-
In Rectangle ABCD,
AD (breadth) = 8cm
AC (diagonal) = 17cm
DC (length) = ?
By Pythagoras theorem -
DC² = AC² - AD²
DC² = 17² - 8²
DC² = 289 - 64
DC = √225
DC (length) = 15cm.
Perimeter = 2(l + b)
→ 2(15 + 8)
→ 2 x 23
→ 46cm
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Question 2.
The area of a semicircle is 1925 cm². Calculate its perimeter.
Answer:-
Area of semicircle =
→ 1925 = 1/2 x 22/7 x r²
→ r² = 1925 x 7/11
→ r² = 13475/11
→ r² = 1225
→ r = 35
Perimeter of semicircle = πr + 2r
→ (22/7 x 35) + (2 x 35)
→ 110 + 70
→ 180cm
-----------------------------
Question 3.
The surface area of a sphere is 5544cm. Find its diameter.
Answer:-
Surface area of sphere = 4πr²
→ 4πr² = 5544
→ 4 x 22/7 x r² = 5544
→ r² = 5544 x 7/ 22 x 4
→ r² = 38808/88
→ r² = 441
→ r = √441 = 21cm.
Radius = 21cm
Diameter = 2r
= 2 x 21
= 42cm