Sasi Math (Revised for 1024)

Scroll:Mensuration >> cylinder and hemisphere >> ps (4135)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 8 cm and the total height of the cup is 14.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

14.5cm

8cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 7 cm and the total height of the cup is 13.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

13.5cm

7cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 6 cm and the total height of the cup is 12.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

12.5cm

6cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 6 cm and the total height of the cup is 11.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

11.5cm

6cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 7 cm and the total height of the cup is 12.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

12.5cm

7cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 5 cm and the total height of the cup is 14.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

14.5cm

5cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 8 cm and the total height of the cup is 10.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

10.5cm

8cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 8 cm and the total height of the cup is 13.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

13.5cm

8cm

___cm²

Answer:_______________

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 6 cm and the total height of the cup is 15.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

15.5cm

6cm

___cm²

Answer:_______________

10)

A cup is in the from of a hemisphere surmounted by a cylinder. The height of the cyllindercal portion is 6 cm and the total height of the cup is 14.5 cm. Find the total surface area of the cup . (take π = $\frac{22}{7)}$

14.5cm

6cm

___cm²

Answer:_______________

14.5cm

8cm

Answer: 592.43cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 8

⇒ r = 14.5 - 8 = 6.5cm

Cylinderical portion:

Height, h = 8

Thus, radius r = 6.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 6.5 x ( 6.5 + 8 )

= 2 x $\frac{22}{7}$ x 6.5 x 14.5

= $\frac{4147}{7}$

= 592.43 cm²

13.5cm

7cm

Answer: 551.57cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 7

⇒ r = 13.5 - 7 = 6.5cm

Cylinderical portion:

Height, h = 7

Thus, radius r = 6.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 6.5 x ( 6.5 + 7 )

= 2 x $\frac{22}{7}$ x 6.5 x 13.5

= $\frac{3861}{7}$

= 551.57 cm²

12.5cm

6cm

Answer: 510.71cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 6

⇒ r = 12.5 - 6 = 6.5cm

Cylinderical portion:

Height, h = 6

Thus, radius r = 6.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 6.5 x ( 6.5 + 6 )

= 2 x $\frac{22}{7}$ x 6.5 x 12.5

= $\frac{3575}{7}$

= 510.71 cm²

11.5cm

6cm

Answer: 397.57cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 6

⇒ r = 11.5 - 6 = 5.5cm

Cylinderical portion:

Height, h = 6

Thus, radius r = 5.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 5.5 x ( 5.5 + 6 )

= 2 x $\frac{22}{7}$ x 5.5 x 11.5

= $\frac{2783}{7}$

= 397.57 cm²

12.5cm

7cm

Answer: 432.14cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 7

⇒ r = 12.5 - 7 = 5.5cm

Cylinderical portion:

Height, h = 7

Thus, radius r = 5.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 5.5 x ( 5.5 + 7 )

= 2 x $\frac{22}{7}$ x 5.5 x 12.5

= $\frac{3025}{7}$

= 432.14 cm²

14.5cm

5cm

Answer: 865.86cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 5

⇒ r = 14.5 - 5 = 9.5cm

Cylinderical portion:

Height, h = 5

Thus, radius r = 9.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 9.5 x ( 9.5 + 5 )

= 2 x $\frac{22}{7}$ x 9.5 x 14.5

= $\frac{6061}{7}$

= 865.86 cm²

10.5cm

8cm

Answer: 165.00cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 8

⇒ r = 10.5 - 8 = 2.5cm

Cylinderical portion:

Height, h = 8

Thus, radius r = 2.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 2.5 x ( 2.5 + 8 )

= 2 x $\frac{22}{7}$ x 2.5 x 10.5

= $\frac{1155}{7}$

= 165.00 cm²

13.5cm

8cm

Answer: 466.71cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 8

⇒ r = 13.5 - 8 = 5.5cm

Cylinderical portion:

Height, h = 8

Thus, radius r = 5.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 5.5 x ( 5.5 + 8 )

= 2 x $\frac{22}{7}$ x 5.5 x 13.5

= $\frac{3267}{7}$

= 466.71 cm²

15.5cm

6cm

Answer: 925.57cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 6

⇒ r = 15.5 - 6 = 9.5cm

Cylinderical portion:

Height, h = 6

Thus, radius r = 9.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 9.5 x ( 9.5 + 6 )

= 2 x $\frac{22}{7}$ x 9.5 x 15.5

= $\frac{6479}{7}$

= 925.57 cm²

10)

14.5cm

6cm

Answer: 774.71cm²

SOLUTION 1 :

Hemispherical portion :

Radius, r = Total height - 6

⇒ r = 14.5 - 6 = 8.5cm

Cylinderical portion:

Height, h = 6

Thus, radius r = 8.5 cm

Total surface area of the cup

= CSA of the hemispherical portion

+ CSA of the cylinderical portion

= 2πr2 + 2πrh = 2πr ( r + h)

= 2 x $\frac{22}{7}$ x 8.5 x ( 8.5 + 6 )

= 2 x $\frac{22}{7}$ x 8.5 x 14.5

= $\frac{5423}{7}$

= 774.71 cm²