Common Core HSG.GMD.A.3 worksheet

Question 1

A model car is built to a length scale of 1 : 3 compared with a bigger model. The small model holds 5 cm³ of paint inside its body. How much would the bigger model hold?

Answer 

Question 2

A cone with the same base and height is drilled out of a solid cylinder (radius 7 cm, height 14 cm). Give the exact remaining volume as a multiple of π.

Answer 

Question 3

Find the surface area of a sphere of radius 4 cm. Give an exact answer in terms of π.

Answer 

Question 4

Find the total surface area of a solid hemisphere of radius 10 cm (curved part and flat face). Give it in terms of π.

Answer 

Question 5

Two similar shapes have lengths in the ratio 1 : 5. The smaller has area 26 cm². What is the area of the larger?

Answer 

Question 6

A rocket model is a cylinder (radius 3 cm, height 13 cm) with a cone (same radius, height 7 cm) on top. Find its volume to 1 decimal place.

Answer 

Question 7

Two similar jugs have surface areas in the ratio 1 : 9. The smaller jug holds 4 ml. How much does the larger jug hold?

Answer 

Question 8

A cone has base radius 10 cm and perpendicular height 24 cm. Find its curved surface area, in terms of π.

Answer 

Question 9

A cone has base radius 6 cm and height 24 cm. The top is cut off parallel to the base, leaving a small cone of radius 3 cm and height 12 cm removed. Find the volume of the frustum that is left, to 1 decimal place.

Answer 

Question 10

A cone of volume 486π cm³ has its top cut off. The removed cone is similar with a length scale factor of 1/3. What fraction of the original volume is left? Give a fraction.

Answer (as a fraction)

Question 11

A capsule is a cylinder of radius 2 cm and length 4 cm with a hemisphere on one end. Find its volume to 1 decimal place.

Answer 

Question 12

A model car is built to a length scale of 1 : 4 compared with a bigger model. The small model holds 9 cm³ of paint inside its body. How much would the bigger model hold?

Answer 

Question 13

A cone with the same base and height is drilled out of a solid cylinder (radius 4 cm, height 12 cm). Give the exact remaining volume as a multiple of π.

Answer 

Question 14

Find the surface area of a sphere of radius 6 cm. Give an exact answer in terms of π.

Answer 

Question 15

Find the total surface area of a solid hemisphere of radius 5 cm (curved part and flat face). Give it in terms of π.

Answer 

Question 16

Two similar shapes have lengths in the ratio 1 : 2. The smaller has area 15 cm². What is the area of the larger?

Answer