Practice Set 7.2
- The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of…
- The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm.…
- The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height…
Practice Set 7.2
Question 1.
The radii of two circular ends of frustum shape bucket are 14 cm and 7 cm. Height of the bucket is 30 cm. How many liters of water it can hold? (1 litre = 1000cm3)
Answer:
The two radii of frustum are, r1 = 14cm and r2 = 7cm
Height of bucket, H = 30 cm
As we know that,
⇒ V = 10780 cm3
Now, as 1litre = 1000cm3
⇒ V = 10.780 litre
∴ Bucket can hold 10.780 litres of water
Question 2.
The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its
i) Curved surface area
ii) Total surface area
iii) Volume
Answer:
(i) The two radii of frustum are, r1 = 14cm and r2= 6cm
Height of frustum, H = 6cm
Slant height of frustum, 
⇒ l = 10
As we know that,
Curved surface area, AC = πl(r1 + r2)
⇒ AC = (3.14) × 10 × (14 + 6)
⇒ AC = (3.14) × 200
⇒ AC = 628 sq. cm
∴ the curved surface area of frustum is 628 sq. cm
(ii) Total surface area, AT = Curved surface area + area of the two circular regions
AT = AC + πr12 + πr22
On substituting the above values, we get,
⇒ AT = 628 + (3.14) × (142 + 62)
⇒ AT = 628 + (3.14)× (196 + 36)
⇒ AT = 628 + 728.48
⇒ AT = 1356.48 sq. cm
∴ the total surface area of frustum is 1356.48 cm2
(iii) As we know,
On substituting the values, we get,
V = 1984.48 cm3
∴ Volume of the frustum is 1984.48 cm3
Question 3.
The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.
Circumference1 = 2πr1 = 132
Circumference2 = 2πr2 = 88
Slant height of frustum, 
Curved Surface area of frustum = π(r1 + r2)l
Answer:
Circumference1 = 2πr1 = 132
Circumference2 = 2πr2 = 88
Slant height of frustum,
Curved Surface area of frustum = π(r1 + r2)l
⇒ Curved Surface Area of frustum = π× (21 + 14) × 25
⇒ Curved surface area = π × 35 × 25 = 2750 sq. cm
