The volume of a cylinder is 448π cm 3 and height 7 cm. Find its lateral surface area and total surface area. - Wired Faculty

Probability

Question

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The volume of a cylinder is 448π cm³ and height 7 cm. Find its lateral surface area and total surface area.

Solution

Let the radius of the base of the cylinder be r cm.
h = 7 cm
Volume = 448 $straight pi$ cm³
$rightwards double arrow space space space space space space space space space πr squared straight h equals 448 straight pi rightwards double arrow space space space space space space space space space straight r squared straight h equals 448 rightwards double arrow space space space space space space space space space straight r squared left parenthesis 7 right parenthesis space equals space 448 rightwards double arrow space space space space space space space space space straight r squared equals 448 over 7 rightwards double arrow space space space space space space space space straight r squared equals 64 rightwards double arrow space space space space space space space space straight r equals square root of 64 rightwards double arrow space space space space space space space space straight r equals 8 space cm$

$therefore$ Lateral surface area = 2 $straight pi$ rh

$equals 2 cross times 22 over 7 cross times 8 cross times 7 equals 352 space cm squared$
Total surface area = $2 πr left parenthesis straight h plus straight r right parenthesis$

$equals 2 cross times 22 over 7 cross times 8 cross times left parenthesis 7 plus 8 right parenthesis$
$equals 2 cross times 22 over 7 cross times 8 cross times 15 equals 5280 over 7 cm squared equals 754.28 space space cm squared.$

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Probability

The volume of a cylinder is 448π cm³ and height 7 cm. Find its lateral surface area and total surface area.

Some More Questions From Probability Chapter

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?

A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m².

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For Daily Free Study Material Join wiredfaculty

Probability

The volume of a cylinder is 448π cm3 and height 7 cm. Find its lateral surface area and total surface area.

Some More Questions From Probability Chapter

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (i) Which box has the greater lateral surface area and by how much?

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (i) Which box has the greater lateral surface area and by how much?

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. (i) What is the area of the glass?(ii) How much of tape is needed for all the 12 edges?

A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The volume of a cylinder is 448π cm³ and height 7 cm. Find its lateral surface area and total surface area.

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

(i) Which box has the greater lateral surface area and by how much?

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m².