Frustum of a Cone | Surface Areas and Volumes | Assessment | English | Grade 10

Which is the correct formula for calculating the Total Surface Area of the frustum of a cone, if height is h, slant height is l and radii of the circular faces are R,r.?

• πl(R +r)

• πl(R +r)+πR²

• πl(R +r)+πR²+πr²

• πh(R +r)+πR²+πr²

Answer explanation

We know that, Total Surface Area = πl(R +r)+πR²+πr² Hence, the correct answer is Option 3.

Radii of the top and the base of a frustum of a cone are 14cm and 8 cm respectively. It's height is 8 cm. The volume of this solid is ___________________.

• 690.8 cm³

• 1507.2 cm³

• 816.4 cm³

• 3114.88 cm³

Answer explanation

We know that, Volume of the frustum = 1/3 πh(R² + r² + R r) = 1/3 x 3.14 x 8 (14² + 8² + 14 x 8) = 3114.88 cm³ Hence the correct answer is option 4.

The perimeter of the circular ends of a frustum are 48cm and 36 cm. if the height of the frustum is 11 cm , find its volume. ( Take π = 22/7)

• 1,050 cm³

• 1544 cm³

• 1554 cm³

• 1,176 cm³

Answer explanation

We know that, Perimeter of a circle = 2πr Let radius of Larger end of frustum = R Let radius of smaller end of frustum = r Perimeter of Larger end = 2πR = 48 cm So, R = 48/2π = 24 /π Perimeter of Smaller end = 2πr = 36 cm So, r = 36/2π = 18 /π We know that, Volume of the frustum = 1/3 πh(R² + r² + R r) h = 11cm, R = 24 /π, r =18 /π V = 1/3 x π x 11( (24 /π)² + (18 /π)² + 24 /π x 18 /π) = 11/3π ( 576 + 324 + 432) = 11/3 x (1332) x 7/22 = 1554 cm³ Hence, the correct answer is Option 3

Bina wants to buy a 20 litre capacity washing tub. The shopkeeper shows her a washing tub. It is in the shape of a frustum of a cone, has height 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively.Should Bina buy this tub or not? ( Take π = 22/7)

• Yes

• No

• Cannot be determined

Answer explanation

We know that, Volume of the frustum = 1/3 πh(R² + r² + R r) h = 21cm, R = 20 cm , r =15 cm Volume of the washing tub = 1/3x 22/7 x 21(20² + 15² + 20 x 15) = 22 ( 400 +225 +300) =22 x 925 = 20, 350 cm³ = 20.35 litres (as 1000cm³) = 1 litre) So, the capacity of the tub is 20 litres approx. and meets Bina's requirement. Hence the correct answer is Option 1

A bucket made of metal sheets is in the form of a frustum of a cone with height 21 cm and radii of it's upper and lower circular ends as 15 cm and 7 cm. Find the cost of metal sheet needed to make the bucket if it costs ₹50 per 100 cm². ( Take π = 3.14)

• ₹. 776.00

• ₹.. 853.00

• ₹.802.00

• ₹.. 835.00

Answer explanation