A frustrum of a right circular cone has a diameter of base $20 c m$ , of top $12 c m$ , and height $3 c m$ . Find the area of its whole surface and volume.

Open in App

Solution

$D_{1} = 20 c m, R_{1} = 10 c m$
$D_{2} = 12 c m, R_{2} = 6 c m$
$h = 3 c m$
Volume of frustum $= \frac{1}{3} π h (R_{1}^{2} + R_{2}^{2} + R_{1} R_{2}) = \frac{1}{3} \times \frac{22}{7} \times 3 [10^{2} + 6^{2} + 10 \times 6]$
$= \frac{22}{7} \times 196 = 616 {c m}^{3}$
Let slant height, be $l$ . Then,
$l = \sqrt{{(R_{1} - R_{2})}^{2} + h^{2}} = \sqrt{{(10 - 6)}^{2} + 3^{2}} = \sqrt{16 + 9} = 5 c m$
TSA of frustum of cone $= π (R_{1} + R_{2}) l + π (R_{1}^{2} + R_{2}^{2})$
$= \frac{22}{7} [10 + 6] \times 5 + \frac{22}{7} (10^{2} + 6^{2})$
$= \frac{22}{7} [80 + 1360] = \frac{22}{7} \times 216 = 678.85 {c m}^{2}$

Suggest Corrections

Similar questions

Q. The radii of the circular bases of a frustum of a right circular cone are

12 c m

and

3 c m

and the height is

12 c m

. Find the total surface area and the volume of the frustum.

The radii of the circular bases of a frustum of a right cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

Q. The diameter of base of a cylinder is

14 c m

and its height is

20 c m

. Find the whole surface area and volume.

The radius of the base of a right circular cone is $21 c m$ and its height is $20 c m$ . Find the curved surface area of the cone.

Q. The volume of a right circular cone is (100π) cm³ and its height is 12 cm. Find its slant height and its curved surface area.

Join BYJU'S Learning Program

A frustrum of a right circular cone has a diameter of base 20cm, of top 12cm, and height 3cm. Find the area of its whole surface and volume.

D1=20cm,R1=10cmD2=12cm,R2=6cmh=3cmVolume of frustum =13πh(R21+R22+R1R2)=13×227×3[102+62+10×6] =227×196=616cm3Let slant height, be l. Then,l=√(R1−R2)2+h2=√(10−6)2+32=√16+9=5cmTSA of frustum of cone =π(R1+R2)l+π(R21+R22) =227[10+6]×5+227(102+62) =227[80+1360]=227×216=678.85cm2

A frustrum of a right circular cone has a diameter of base $20 c m$ , of top $12 c m$ , and height $3 c m$ . Find the area of its whole surface and volume.