Q17 of 56 Page 13

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of the bucket is 5390 cm3, then find the value of r. [Use π =](CBSE 2011)

The bucket is in the shape of a frustum of a cone.

Given: h(height) =15cm


R(larger) =14cm
r(smaller)= r cm(assume)


Volume of frustum of cone =cm3 (given)


⇒


⇒


⇒r2 + 14r + 196=343


⇒ r2 + 14r + 196-343=0


⇒ r2 + 14r-147=0


⇒ r2 + 21r-7r-147=0


⇒ r(r + 21) -7(r + 21)=0


⇒ (r-7)(r + 21)=0


There are two values of r possible r = 7 and r = -21


r=-21(neglected as negative value of r is not possible)


∴ r=7cm.

More from this chapter

All 56 →
15

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?(CBSE 2017)

 16

An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at Rs. 30 per litre.

Use π = 22/7. (CBSE 2011)

 18

From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid. (CBSE 2011)

 19

The radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area. [Use π = 3.14.] (CBSE 2011)