FIND HEIGHT OF CONE FROM THE GIVEN SURFACE AREA WORKSHEET

Find slant height of the following cones given below.

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

Find the volume of the cone 

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Problem 8 :

find the missing dimension(s) when Volume = 75.4 cm³

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Problem 9 :

A cone has a diameter of 11.5 inches and a slant height of 15.2 inches

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Problem 10 :

A right cone-shaped funnel has a height of 8 centimeters and a diameter of 4.8 centimeters. Find the volume of the cone and slant height.

Solution

Problem 11 :

A cone has height h and a base with radius r. You want to change the cone so its volume is doubled. What is the new height if you change only the height ? What is the new radius if you change only radius ?

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Problem 12 :

A glass in the shape of a right cone has a diameter of 3.3 inches and a slant height of 5.5 inches. Find the height of the cone.

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Problem 7 :

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Problem 8 :

Problem 3 :

Find what length of canvas 3/4 m wide is required to make a conical tent 8 m in diameter and 3 m in high.

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Problem 4 :

Four right circular cylindrical vessels each having diameter 21 cm and height 38 cm are full of ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape at the top. Find the total number of such cones which can be filled with ice-cream.

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Problem 5 :

The base radius and height of a right circular solid cone are 2 cm and 8 cm respectively. It is melted and recast into spheres of diameter 2 cm each. Find the number of spheres so formed

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Problem 6 :

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 6 cm and its height is 4 cm. find the cost of painting the toy at the rate of $5 per 1000 cm².

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Problem 7 :

A corn cob shaped somewhat like a cone has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1𝑐𝑚² of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob.

Solution

Problem 8 :

The curved surface area of a cone is 12320 sq. cm, if the radius of its base is 56 cm, then its height is

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Problem 1 :

Total surface area of a cone whose radius as p/2 and slant height as 2l is:

(a) 2πp(l + p)                       (b) πp(l + (p/4))

(c)  πp(l + p)                         (d) 2πpl

Solution

Problem 2 :

If the slant height of a cone 12 cm and radius of the base is 14 cm, then the total surface area is.

Solution

Problem 3 :

The radius and height of a cone are in the ratio 4:3. The area of the base is 154 cm². Find the curved surface area

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Problem 4 :

There are two cones, the curved surface area of one cone is twice that of the other. The slant height of later is twice that of the former. Find the ratio of their radii

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Problem 5 :

How much material is needed to make the Nón Lá Vietnamese leaf hat? Find the height.

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Problem 6 :

A paper cup shaped like a cone has a diameter of 6 centimeters and a slant height of 7.5 centimeters. How much paper is needed to make the cup?

Solution

Problem 7 :

The total surface area of the cone is 100𝛑 square meters and radius is 5 m. What is the slant height of the cone.

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Problem 8 :

A right cone has a base radius of 4 m and a height of 10 m. Calculate the surface area of this cone to the nearest square meter.

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Problem 9 :

Aiden built a cone-shaped volcano for a school science project. The volcano has a base diameter of 32 cm and a slant height of 45 cm.

a) What is the lateral area of the volcano to the nearest tenth of a square centimeter?

b) The paint for the volcano’s surface costs $1.99 jar, and one jar of paint covers 400 cm². How much will the paint cost?

Solution